It means time to quit, to give up. I believe this phrase comes from baseball, where spikes are referring to the spikes (also called cleats) on the bottom of the shoes which help the players run faster. So basically you're saying that it is (or was) time to hang up your shoes.

"Spikes" refers to the sports shoes with spikes worn by atheletes. The spikes obviously give better traction. When an athelete "hangs up his spikes [sports shoes]", it means he is retiring from active play. Sometimes it is used figuratively for a person that is not an athelete when they retire from active duty on some job.