Vector Spaces expressions When a vector space is just a set of vectors just like any other linear space . Then why is it that you always need a basis to express vectors ?
For example , you don't generally need a basis to express the elements of the set of real numbers , like you don't see someone expressing (4) as '4' x (1) always. Where (1) is the basis and '4' is the scalar and (4) is the element of linear  space of real numbers .
but for vectors you need to resolve the vector into components of the basis . Why ?
And why is this thing called a " Space " ?
And I think I understand what a number is , but what is a vector ? Or in fact what is even a number ?
 A: You don't have to use bases, they just make your life easier when dealing with vector spaces. Since $\mathbb{R}$ is one dimensional, the notion of basis is not that useful. As you pointed out, you don't gain much from writing $4$ as $4\cdot 1$, taking $1$ as a basis of $\mathbb{R}$. More generally, when dealing with some sort of structure or collection of objects it is useful to decompose the structure or collection of objects into smaller more fundamental components (or "building blocks"), such that all the elements of your structure or collection are just certain combinations of these more fundamental building blocks (for a non-mathematical analogy think of say the periodic table of elements in chemistry). So even though finite dimensional vector spaces over the real or complex numbers have uncountably many elements, the situation is simplified dramatically once we can identify a linearly independent set of vectors which span the space, then we know that all other vectors are just certain combinations of these fundamental "building blocks".
As for why vector spaces are called spaces, it's just because once a basis is chosen we can think of them in a geometric way just as we do with $\mathbb{R}^n$ or $\mathbb{C}^n$. You don't have to think of vector spacers as spaces if you don't want, but if you like to use your visual sense at all when thinking of mathematical structures (as I do) then thinking of vector spaces as actual "spaces" enables one to use their geometric intuition along with the algebraic formalism.  
A: You think you always need a basis because you do not know enough examples. Perhaps the definition of a vector space over $\mathbb R$ would make things clearer. 
A set $V$ together with operations $+ : V \times V \to V$ and $\cdot : \mathbb R \times V \to V$ is called a vector space over $\mathbb R$ if they satisfy these properties :
$$
\forall a,b,c \in V, \quad  a+b = b+a, \quad a+(b+c) = (a+b)+c, 
$$
and there exists $0 \in V$ such that $\forall a \in V, a+0 = a$. Furthermore, for each $v \in V$, there exists another vector called $-v$ such that $v+(-v) = 0$. For the scalar multiplication, we require 
$$
1 \cdot v = v, \qquad r \cdot (s \cdot v) = (rs) \cdot v, 
$$
and distributivity from both sides : 
$$
r \cdot (v_1 + v_2) = r \cdot v_1 + r \cdot v_2, \qquad (r_1 + r_2) \cdot v = r_1 \cdot v + r_2 \cdot v.
$$
If you have something like this, it's called a vector space. You don't need a basis to express its elements. For instance, if you take the space of all functions from $\mathbb R \to \mathbb R$, they can be added ($(f+g)(x) = f(x) + g(x)$ is the definition of the sum of two functions), they all have inverses (the zero of this space would be the $0$ function) and multiplication by scalar is defined as $(\lambda f)(x) = \lambda (f(x))$. The properties are all satisfied, hence you have a vector space. 
Note that this example is infinite dimensional (in the simple sense that it doesn't admit a finite basis). In infinite dimension, the discussion of bases is less trivial than in finite dimension. 
A number usually stands for an element of $\mathbb R$, but for some people a number can also mean a complex number (i.e. an element of $\mathbb C$), so you need to notice the context. A vector stands for an element of a vector space, so saying that something is a vector refers to the vector space it lives in.
Hope that helps,
