Parsing means determining the syntactic structure of an expression, that is written according to the rules of a certain grammar. Suppose you are writing a calculator. You are fed a string like 17*(6+3/7)+sqrt(90+20/2). In order to evaluate that expression (and I don't mean just feeding it to eval), you have to parse it according to the rules of the grammar, which might be the BODMAS rule (brackets of division, multiplication, addition & subtraction).
To parse that expression, you have to break it down into tokens (17, *, (, 6, +...) and verify that it adheres to the rules. Having done that, you can then start to process the data.
in reply to What does the word "parse" mean?
You usually parse something that can be very free-form in nature. For instance, you don't really parse the format of Unix's /etc/passwd password file, because it has a very rigid definition. Fields are delimited by colons, and each field has a precise defined purpose. You do, on the other hand, have to parse an SQL statement.
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