These guys are absolutely right. To take the example further, lets say you have this math expression:
in reply to What does the word "parse" mean?
when you parse this, it becomes
So parsing something really is about breaking it down into its individual chunks and pieces. For instance, a parser might break your c++ program into functions, or your word into letters. If you have a whole made of parts, the parser looks at those parts. Make sense? Check out the definitions linked above, they're probably better at explaining it than I am. Hope that helped a little.
PS The above is a "parse tree", certainly not the only way to parse or represent a parse. Just so you know.