Supression assists

To explain it, I will have to describe what suppression is first.

In Battlefield 1, shots that barely miss the target will induce an effect called suppression - it results in slightly blurred vision, weapon swaying around more and extra recoil and spread. Different weapons can cause different amounts of suppression - generally, light machine guns and Scout rifles will suppress enemies stronger than submachine guns, shotguns or self-loading rifles. Distance matters too - targets further away from the shooter are suppressed faster.

Now, to the question: suppression assist is given when the enemy that you have suppressed was killed by your teammate. You will get a small point bonus for that. Squad suppression assist happens when your squadmate kills the enemy you have suppressed.

I hope that explains it well enough.