Kicker
A kicker is a side card in your hand that doesn't form part of your main pair, trips, or other combo but breaks ties when two players share the same rank.
In Texas Hold'em, a poker hand is always five cards, but the cards that actually make your hand (like a pair) don't always use up all five slots. The leftover high cards that fill out those slots are your kickers. They sit quietly until two players end up with the same made hand, and then the highest kicker wins the pot.
This comes up most often when two players pair the same card on the board. Say you both pair the ace; whoever holds the better second card wins. The kicker is also why hands like ace-king are so much stronger than ace-five even though both are just ace-high until you pair, because if an ace flops, your king plays as a strong kicker.
For beginners, the big lesson is to respect your kicker before you get attached to a weak pair. A small kicker is a common way to lose a chunk of chips in what's called a dominated hand. When you pair the board with a weak side card, slow down, since someone with the same pair and a bigger kicker can quietly out-rank you and win at showdown.
Example
You hold A9 and an opponent holds AK; the flop comes A-7-2, so you both have a pair of aces but their king kicker beats your nine, and if all the chips go in, they win the pot.