Definition
Outs are the unseen cards that will complete your drawing hand and (likely) give you the best hand. Counting outs is one of the first skills a developing poker player learns, because it enables rough equity calculations without a computer.
A common approximation for equity using outs is the "Rule of 2 and 4": multiply your outs by 4 with two cards to come (flop), or by 2 with one card to come (turn), to get an approximate equity percentage.
Common out counts: flush draw = 9 outs (~35% to hit on the turn or river combined), open-ended straight draw = 8 outs (~31%), gutshot = 4 outs (~16%), two overcards = 6 outs (~24%). These estimates are starting points; the quality of outs matters, as some may give your opponent a better hand even when they improve yours.
Example
You hold 8♦9♦ on a K♦5♦2♣ flop. You have 9 flush outs and 8 straight outs (6s and Ts), minus overlap — approximately 15 clean outs, giving you roughly 54% equity to improve to the best hand by the river.