The abbreviation "w/" is generally a shortened version of the word "with." Similarly, most people use either "w/o" or "w/out" to abbreviate the word "without."
People use these abbreviations for taking notes or writing in other informal formats. They are part of a system of shorthand writing that facilitates writing things quickly, and the abbreviations come in handy when someone is speaking and note-takers are having trouble keeping up with the spoken words. The abbreviations "w/" and "w/o" are not generally acceptable on essays, reports or any other formal project. Shorthand is not typically considered to be appropriate in professional writing.