A flanker is a German unit that has successfully pierced your defenses by crossing the bottom line of the map, or that has been left behind while advancing. They are indicated by little crosses at the bottom. If 10 of them pass through, you lose the game!
Most units only count as 1 flanker, including vehicles, with the notable exception of the Zündapp KS750, who counts as 1 if the gunner is dead, and 2 if both the gunner and the driver are alive, and if both the gunner and driver are shot out and the bike rolls past your lines, the bike itself will count as a flanker. The Goliath, Kubelwagen, and FlaK 38 do not count as flankers.
The main way to remove them is through an ability that the Officer possesses, though you cannot control it – he uses it randomly. Otherwise, if you're lucky, you can get flanker reductions from crates, but this is presumed to only work during the Airborne Challenge.
Flankers are gone from the field forever, but not gone from the game - they can still stage highly dangerous Unfair Events against you! They start staging Unfair Events after wave 50.