deg. is only the short written form of degree or degrees. You meet it in notes, tables, science work, and weather — anywhere someone is saving space on the page. Most often it marks how hot or cold something is (20 deg. C, 32 deg. F) or how wide an angle is (a 90 deg. corner). Though actually, printed books more often use the little circle °; deg. is what people type when they cannot make that mark, or when a form wants plain letters. The same full word degree also names a school paper (a master's degree), and old lists sometimes shorten that to deg. too, but everyday writing usually spells the school meaning out. It is not a spoken word: you still say "degrees." In a normal sentence it feels a little cramped and old-fashioned; write the whole word unless you are filling a table.