1550s, "to state the parts of speech in a sentence," verb use of Middle English pars (n.) "part of speech" (c.1300), from Old French pars, plural of part "part," from Latin pars (see part (n.)) in school question, Quae pars orationis? "What part of speech?" Transferred (non-grammatical) use is from 1788. Pars was a common plural of part (n.) in early Middle English. Related: Parsed; parsing.
An algorithm or program to determine the syntactic structure of ("parse") a sentence or string of symbols in some language. A parser normally takes as input a sequence of tokens output by a lexical analyser. It may produce some kind of abstract syntax tree as output. A parser may be produced automatically from a grammar by a parser generators such as yacc.
A parser is normally part of some larger program, like a compiler, which takes the output of the parser and attempts to extract meaning from it in some way, e.g. translating it into another language.