I think it means that if you pair your kicker, it doesn't help someone get a better hand than your two-pair.

e.g. You have A7s, with a Axx flop (where x is not 7) and a 7 hits the board but it doesn't give anyone else trips, a straight or a non-heart flush. Then, one would say your kicker is live.

A counter example: You have AJs, and the board is AKT, but your opponent has a Q .... Now J hits the board pairing your kicker but it just gave your opponent a broadway str8. Now (assuming no flush or str8 potential for you) your only escape hatch is another J or A for a boat.