Kickers are the leftover cards used to determine who wins, if more than one player has the same hand after the showdown. Not all hands have "leftovers." Kickers only apply to four-of-a-kind, three-of-a-kind, two pair, one pair, and high card situations.
In Texas Hold'em, a player always uses the best combination of five cards. There can only be a certain number of kickers, see examples below.