Kicker
The side card that breaks ties between two players with the same hand. The silent cause of most "bad luck" hands.
The kicker is the card riding along with your hand that settles the tie. On an A♣7♦2♠ board, both A♥K♦ and A♠Q♠ have a pair of aces — the kicker decides: the K beats the Q and takes the whole pot.
Domination, in numbers
This situation is called being dominated: you share the good card and lose on the second one. It’s one of the worst spots in poker, and the engine puts an exact number on it: AK against AQ is 74.0 / 26.0 before the flop. The dominated hand only escapes by pairing its kicker (while you miss yours) or by backing into a straight or flush.
The treacherous part is that domination is invisible: when the ace hits the flop, both players think they have the best hand, and the loser tends to pay all the way down. Most top-pair “coolers” are exactly this.
The lesson for your starting hands
The kicker is the mathematical case against “pretty” hands like A5o or K8o: they make the same pair as AK, but every time the pot gets contested they show up with the losing tiebreaker. That’s why the trainer’s opening ranges demand a decent kicker for high-card hands — and why A5 suited does make the cut: its arguments are different (nut flush, the wheel, blockers), not the pair of aces.