adv. is the written short form of adverb. In dictionaries and grammar notes, you see it next to words like quickly, very, or yesterday, to show that the word tells you how, when, where, or how much. You write it with a full stop: adv. It belongs on the page, not in speech — nobody says “adv” when they talk. Though actually, the same letters can stand for other things in other kinds of notes, so this meaning lives in grammar and dictionaries.