In normal English usage, we use the word grammar to mean either reference material regarding how a language is used (descriptive grammar) or rules of correct usage (prescriptive grammar).
Acquisition researchers use the term in a third sense: your grammar is your underlying competence in the language, or what you subconsciously 'know' about what is possible and impossible in it. A grammar is therefore an idealized, individual and internal representation of a language. The notion of an idealized grammar or competence is useful to abstract away from performance errors, such as slips of the tongue, which occur during actual language use.
Each speaker possesses his or her own
'mental grammar' consisting of a lexicon that provides information about the linguistically relevant properties of words and a computational system that is responsible for the formation and interpretation of sentences.
First and second language speakers of a language possess grammars for these languages, and second language learners construct their individual interlanguage grammars on the basis of the linguistic input they are exposed to - what they hear or read, or what they are taught.
Researchers are interested in how interlanguage grammars are constrained, or why learners never make certain kinds of mistake. The question of evidence is of interest in this respect.