Some confusion about Theory of Sets by Bourbaki On page 16 :

"A mathematical theory contains rules which allow us to assert that certain assemblies of signs are terms or relations of the theory"

Originally, I simply regard 'rule' as manipulation on assembles with or without property (here 'manipulation' means operation which gain a new assemble, property means character which can be judged precisely). For instance, $\lor AB$. where $A,B$ represent two normal assemblies (without property), $\lor$ can be regard as an assemble with certain property which allow us to judge that general assemble if it is $\lor$.
On page 25 :

"R results from the application of a scheme to terms or relations".

However, for S1 on page 28, '$\lor$' can't be term or relation.
In a word, I want to know the precise definition of "rule".
 A: As Asaf says : "Why are you reading about set theory from Bourbaki ?".
In general, I think that Bourbaki is not a good point to start with regarding both set theory and mathematical logic.
In general, taken aside the "un-friendly" symbolism used by Bourbaki, the starting point for "formalizing" mathematics (as you can find in modern mathematical logic textbooks, like Herbert Enderton, A Mathematical Introduction to Logic (2nd ed - 2001) ) are :

a language, base on a finite set of symbols and rules (mechanically checkable) for building allowable expressions, tipically called terms and (well formed) formulae (Carnap called them "formation rules").

So, reading from the french edition of Nicolas Bourbaki, Théorie des ensembles (1970), your citation points at the definition of term (i.e. a "name" denoting an object of the "universe of discourse" of the theory; e.g. in number theory, $0$, $1$, ... are "names" for numbers) and formula (relation), an expression about the objects of the domain and their properties that has a definite meaning (e.g.in number theory, the sentence $0 < 1$, that is true).
See on page I.18 of french edition :

" Intuitivement, les termes sont des assemblages qui représentent des objets, les relations sont des assemblages qui représentent des assertions que l'on peut faire sur des objets. "

The language of Bourbaki use only two connectives : $\lnot$ (negation) and $\lor$ (disjunction) [see page I.14] and define the conditional ($\Rightarrow$) in the usual truth-functional way [see page I.15].
What makes "terrible" the reading of Bourbaki, is the use of Hilbert's epsilon operator in place of quantifiers, where a term $\epsilon x A$ denotes some $x$ satisfying $A(x)$; see epsilon calculus, with the added difficulty due to the omission of bounded variables, replaced by a "square" as place-holder [see page I.16].
The second component of a formalized system is :

a set of primitive expressions called axioms (like Euclid's postulates for geometry); we assume them as expressing "true facts" about the "universe of discourse" of our system (like $a + 0 = a$ in number theory).

The third component will be :

a set (tipically one : modus ponens) of inference rules applicable to existing formulae to "produce" new formulae (Carnap called them "transformation rules").

With this machinery in place, you can have the fundamental definitions of :

derivation, i.e. a finite sequence of formulae where each step is an axiom or is obtained from previous formulae in the sequence by use of the inference rules
theorem, i.e. the last formula in a derivation.

So, a derivation is a (formal) proof in the system and a theorem is a formula that has been proved in the system starting from the axioms.
Note. The "$\lor$" is simply the disjunction; see page I.18 :

Remarque. — La condition [...] b) signifie que, si $B$ est une assertion, $\lnot B$, qu'on appelle la négation de $B$, est une assertion (qui se lit: non $B$). La condition c) signifie que, si $B$ et $C$ sont des assertions, $\lor BC$, qu'on appelle la disjonction de $B$ et $C$, est une assertion:

Subsequently, $\lor$ "disappear" because Bourbaki introduces some useful abbreviations [page I.21] :

"Pour faciliter la lecture de ce qui suit, nous écrirons désormais, si $A$ est une relation, non($A$) au lieu de $\lnot A$. Si $A$ et $B$ sont des relations, nous écrirons « ($A$) ou ($B$) » au lieu de $\lor AB$, et ($A$) $\Rightarrow$ ($B$) au lieu de $\Rightarrow AB$. Parfois, nous supprimerons les parenthèses. Le lecteur pourra déterminer sans peine [sic !], dans chaque cas, de quel assemblage il s'agit."

