The strength of a non-paired card in your hand. An ace is the strongest kicker, a 2 is the weakest kicker and so-forth. If multiple players have the exact same strength of hand at the showdown, kickers are compared to determine the winner.
Example: You hold, AT on the board A9744 at showdown
Your opponent holds AQ
Your opponent has a better kicker, and will win the entirety of the pot because of the kicker.