Neg. is the written short form of negative. You see it in notes, forms, lab reports, and dictionaries, where there is little space. What 'negative' means depends on the paper in front of you: a blood test marked neg. usually means the thing they looked for was not found (often good news); in grammar, neg. can mark a 'no' word; in maths or science it can mean a minus value. People almost never say 'neg' out loud in careful speech; they read it as 'negative'. Though actually, in some labs and hospitals staff do mutter 'neg' when they are rushing through a list. It is not a full word you put in an essay.