Fight for your life is what happens when all of your health is depleted and your downed by enemies. In this state you can either kill enemies to 'fight' your way back up or be revived by a coop partner, to do this simply walk over them and hold
Now for the coop bit you can either do this over xbox live or locally so long as the accounts that you're reviving are on your friends list, both of you need to have friended each other and not just one of you has friended else you're just a follower of that account.
Obi Jase has commented saying that the accounts should only friend each other and not have them set as a favourite. DoonDoons recommends that both of you need to be showing as online as well, just in case.
Here's a video using 2 controllers (Using gameDVR)
Phone version with pop for odiedodie