Kicker is a definition used in poker to denote a card in a hand “that does not itself take part in determining the rank of the hand, but that may be used to break ties between hands of the same rank.” Since in Texas Hold’em it is common to match only one of your hole cards with one or more from the board, the other usually takes the role of the kicker.
In each hand, the strongest five cards are taken into consideration when determining the winner. In case, for example, you had AT and your opponent had A9 on a board of A-Q-7-5-3, you were the favourite as the best combination would be A-A-Q-T-9 in which you held A and T while your opponent had “only” A and 9. If, however, the board was, say, A-K-Q-J-6, both of you had A-A-K-Q-J as the best combination, meaning the pot would be split.
Here is a training video from PaddyPowerPoker.com Poker School to show you how kickers can benefit you and how they can be deceptive.