What's this "decertification of the player's union" about?

Every day, I see another NFL team voting to decertify the union to thwart a lockout. What exactly does this mean? Does this mean the union will cease to exist? How will that effect if there’s a lockout or not?

Quoth the AP:

But suppose the union decertifies, and then management calls off the lockout. Wouldn’t teams then be able to sign players one at a time, as individuals, at whatever salary and terms they would agree to? How could that possibly be good for the players?

Could be very good for Peyton Manning, for example. Can you imagine a bidding war for him? Not so good for the guys at the other end of the spectrum, though.

Most players are already under contract.