How could a statement be true without proof? Godel`s incompleteness theorem states that there may exist true statements which have no proofs in a formal system of particular axioms. Here I have two questions;
1) How can we say that a statement is true without a proof?
2) What has the self reference to do with this? Godel sentence "G" can say that SUB(a,a, no prove) but could be this just arbitrarily judgement about non-provability of "a" because it may simply has a proof which is not yet revealed or discovered?
 A: Your confusing stems from the way many articles about Godel's incompleteness theorems are extremely imprecise. Here is a proper definition.
$\def\nn{\mathbb{N}}$

We say that a sentence $φ$ over a language $L$ is true in an $L$-structure $M$ iff $M \vDash φ$.
For convenience, when $L$ is the language of arithmetic, we say that $φ$ is true iff $\nn \vDash φ$.

Note that these definitions are only possible in a meta-system that already has a collection called $\nn$ (also known as the standard model of PA). Thus:
$\def\t#1{\text{#1}}$
$\def\con{\t{Con}}$
$\def\pa{\t{PA}}$

"$φ$ is true but unprovable" is more precisely "$\nn \vDash φ$ and $\pa \nvdash φ$".

Now there is a sentence over PA denoted by $\con(\pa)$ such that PA is consistent iff $\nn \vDash \con(\pa)$ (in other words PA is consistent iff $\con(\pa)$ is true in the standard model). It is in fact non-trivial to show that such a sentence exists, which is a crucial part of Godel's first incompleteness theorem.
The remainder of the incompleteness theorem shows that $\pa \nvdash \con(\pa)$. But the meta-system we choose always has $\nn \vDash \pa$, so $\pa$ is consistent and hence $\nn \vDash \con(\pa)$. Thus $\con(\pa)$ is the first natural example of a sentence that is true but unprovable (in the precise sense defined above).
Note that it is false that every true but unprovable sentence $φ$ can be proven by $\pa+\con(\pa)$. In particular, $\pa+\con(\pa) \nvdash \con(\pa+\con(\pa))$, even though $\nn \vDash \con(\pa+\con(\pa))$ (by essentially the same argument as above). This can be proven simply by applying Godel's proof of the incompleteness theorem to $\pa+\con(\pa)$.
Better still, we can let $\pa_0 = \pa$ and recursively let $\pa_{k+1} = \pa_k + \con(\pa_k)$ for every $k \in \nn$, and then let $\pa_ω = \bigcup_{k\in\nn} \pa_k$. Then we still have $\nn \vDash \pa_ω$, and yet $\pa_ω \nvdash \con(\pa_ω)$ even though $\pa_ω \vdash \con(\pa_k)$ for every $k \in \nn$.
A: *

*Assuming your formal system is consistent, Gödel shows there is a statement in that system whose interpretation is true but that is unprovable in the system.  The statement is actually provable, but not in that system: you need the additional assumption that the system in consistent, and that is not provable in the system (unless the system happens to be inconsistent!).

*There's no "arbitrarily judgement" here. If there were a proof of "a", you could use that to produce a proof of 0=1. Thus if the system is consistent, "a" is not provable in the system.
A: 
1) How can we say that a statement is true without a proof?

The main idea behind the standard definitions of truth used by most mathematicians and logicians that study mathematical logic, model theory and related topics is the one given by Tarski. As you can see at the link, he separated the concept of truth from the syntax of the language (for a good number of reasons, e.g., to not allow statements such as "this statement is false"), i.e., the truth concept is not given within the language but by the metalanguage. As the concept of proof is syntactical, at first you won't need any proved formula to be true or any true formula to be provable, but there's a property called soundness and it gives the following result: 
In a first order theory, if $\Sigma \vdash \varphi$ then $\Sigma\vDash \varphi$.
First, $\Sigma \vdash \varphi$ means that a set of formulas $\Sigma$ can prove the formula $\varphi$, i.e., you have $\Sigma$ and logical axioms (and, maybe, some aditional nonlogical axioms from the theory) as assumptions and are able to derive or deduce $\varphi$ using the rules of inference of your theory, so this is a syntactical process. Now, in my notation, $\Sigma \vDash \varphi$ means that all structures (which carry the concept of truth) that satisfy the formulas in $\Sigma$ also satisfy $\varphi$, in other words, if all formulas in $\Sigma$ are true in some structure $\mathfrak{M}$, then $\varphi$ must be true in $\mathfrak{M}$. As $\Sigma$ usually is a set of axioms that define a theory, if $\mathfrak{M}$ is a structure that satisfies $\Sigma$ (i.e., all formulas in $\Sigma$ are true in $\mathfrak{M}$) we say that $\mathfrak{M}$ is a model of $\Sigma$. In his doctoral dissertation , Gödel proved the converse, which is known as his Completeness Theorem:   
In a first order theory, if $\Sigma \vDash \varphi$ then $\Sigma\vdash \varphi$.
We say that a theory is complete in that sense (some authors call it semantically complete, to not make confusion with other type of completeness that is used in the Incompleteness Theorems, which they may call syntactical completeness) if this statement is valid (and it is, Gödel proved it). 
Now we can observe the fact that in some theories there are statements that can't be proved as well as their negation, you don't need to go too far to have some examples of this happening, if you have a system where you axioms $\Sigma$ are the Field Axioms you can't prove the formula $\varphi$ where it is $(\exists x)(x^2=-1)$ for the following reason: we can see (in a not rigorous manner) both $\mathbb{C}$ and $\mathbb{R}$ as models of $\Sigma$ and $\varphi$ is true in $\mathbb{C}$ (as you can take $x=i$) and false in $\mathbb{R}$, which means that not all models of $\Sigma$ satisfy $\varphi$, i.e., $\Sigma \nvDash \varphi$ and, by the soundness property, we have that $\Sigma \nvdash \varphi$ and, with a similar argument, you also have that $\Sigma \nvdash \neg \varphi$. 
Now that we know that there are some theories that have statements that you can't prove (as well as their negation), we call such systems incomplete (or, as I commented early, syntactically incomplete), what Gödel showed in his First Incompleteness Theorem was that any first order theory that satisfy some conditions will be incomplete, and that proved that, because the way mathematicians axiomatize the standard mathematical theories, we can't scape from the fact that there will always be statements such as $\varphi$ I showed early. In particular this will be valid for some theories that have a set of axioms $\Sigma$ with some properties and such that $\textbf{PA}\subset \Sigma$ where $\textbf{PA}$ is the set of Peano's Axioms.
On the other hand, mathematicians suppose that there's a standard model for arithmetics, i.e., a structure $\mathfrak{N}$ that satisfies $\textbf{PA}$ and every arithmetical statement, to be considered true, must be satisfied in that structure. Now I can finally give you an answer to your question: by the First Incompleteness Theorems, loosely speaking, any system of axioms $\Sigma$ (given some conditions) for the standard arithmetic will have statements $\varphi$ such that  $\Sigma \nvdash \varphi$ and  $\Sigma \nvdash \neg \varphi$, but $\mathfrak{N}$ satisfies $\varphi$ or $\neg \varphi$, that means that there will always be a true statement (a formula satisfied by $\mathfrak{N}$) that can't be proven by a given system of axioms $\Sigma$.

2) What has the self reference to do with this? Godel sentence "G"
  can say that SUB(a,a, no prove) but could be this just arbitrarily
  judgement about non-provability of "a" because it may simply has a
  proof which is not yet revealed or discovered?

The self-reference is just an argument used by Gödel in his original proof from which he was able to construct a sentence that is not provable by the system and will be true when you see it with the lens of the meta-theory. With all I said I hope you can comprehend that some statements in a given fixed theory are impossible to prove, it's not a matter of something not being revealed or discovered. 
For further reference and lots of details and technicalities that are missing in my answer, as well as aspects of the problem consisting on deciding if a statement is true or not, I can recommend the following textbooks:


*

*Hinman, Peter G. Fundamentals of Mathematical Logic. Wellesley, MA: A.K. Peters, 2005. 

*Dalen, Dirk. Logic and Structure. Fifith Edition. Berlin: Springer-Verlag, 2013

*Tourlakis, George. Lectures in Logic and Set Theory. Vol. 1, Mathematical Logic (Cambridge Studies in Advanced Mathematics ; 82). N.p.: Cambridge UP, 2003. 

*Shoenfield, Joseph R. Mathematical Logic. Reading, MA: Addison-Wesley Pub., 1967. 
There are also good references and links here and here.
A: As is convenient in discussions of the completeness theorems, let's focus on the theory of arithmetic over the natural numbers. We have a well-defined notion of truth in the natural numbers under the usual arithmetic operations: e.g., the sentence $\forall i\cdot \exists a, b, c\cdot \ a > i \land a^2 + b^2 = c^2$ asserts the existence of arbitrarily large Pythagorean triples and we "know" what that means (specifically it means that it is valid in what model theorists call the structure comprising the natural numbers and the usual arithmetic operations).
Now let's think about methods for deducing which sentences are true in this theory, e.g., we might take our method to be first-order logic and Peano's axioms. What  Gödel's incompleteness theorem says is that (under some very reasonable hypotheses on the method), there is no method that will let us deduce all true sentences and no false sentences. The theorem does not say "there is no proof", it says "a specific method of finding proofs will never find one".
The philosophical interest is that the theorem applies to an enormous range of "specific methods of finding proofs" and indicates that there is no chance of finding an adequate foundation system for mathematics that can prove its own consistency. 
