Simple explanation: Parsing is breaking a block of data into smaller pieces (tokens) by following a set of rules (using delimiters for example), so that this data could be processes piece by piece (managed, analysed, interpreted, transmitted, ets).
Examples: Many applications (like Spreadsheet programs) use CSV (Comma Separated Values) file format to import and export data. CSV format makes it possible for the applications to process this data with a help of a special parser. Web browsers have special parsers for HTML and CSS files. JSON parsers exist. All special file formats must have some parsers designed specifically for them.