Here's and example where kickers come into play:
You hold AK offsuit.
Your opponent has A6 offsuit.
The board at the end od the hand is Q-A-Q-3-7.
Your best 5 card hand is A-A-Q-Q-K,
Your opponents is A-A-Q-Q-7.
You have the better kicker card (The King), so you would win the hand even though you both would have two pair (Aces and Queens).
In the last example if you had A2,
And your opponent had A6,
And the board was Q-A-Q-3-7.
Both of you would have the same hand (A-A-Q-Q-7), so there would be a split pot.