When your partner gets grabbed they’ll need help and it will be indicated by a flashing red circle. Run towards them and hit when the button prompt appears. Rescuing your partner is when your partner runs out of health and you need to help them up before they recover on their own.
If you’re playing solo, your partner never runs out of health, but they will get grabbed occasionally. You should be able to unlock this partway through the campaign. If not, you can do it by yourself in split-screen or online with a friend.