What are the front teeth on some slip joint pliers actually for?

The teeth on the front tip of the jaws are a real thing and they work. I've got a pair of pliers with that front grip feature and they've saved me on rounded off faucet nuts and old supply line fittings more than once. The idea is that the little teeth are angled so when you squeeze, they dig into the head instead of just sliding off the way smooth jaws do. On a badly rounded bolt like yours, that bite is the difference between getting it out and making things worse. That said, for your sink drain bolt specifically, I might try something else first. If the head is really chewed up, a bolt extractor socket works better than any pliers. You tap it on and it grips in reverse as you turn counterclockwise. Harbor Freight sells a set cheap and they work fine for this kind of thing. You could also hammer on a slightly smaller socket or cut a slot in the head with a hacksaw and use a flathead screwdriver. A penetrating oil soak beforehand helps a lot too, especially anything near a water heater where things have corroded solid. For the water heater job, the front teeth thing is genuinely useful but honestly a good pair of regular tongue and groove pliers with fresh teeth plus penetrating oil will handle most of it. The specialty grip pliers shine on small stuff, like stripped screws and tiny bolts where there's not much metal left to grab.

So yes, legit feature, not a gimmick. But for this particular bolt I'd grab an extractor socket before spending money on a new tool. If you keep doing plumbing work though, the pliers are a nice addition to the bag. They fill a gap nothing else really covers.

Agreed on the front teeth thing, they're not just for show. I used mine on a corroded packing nut under an outdoor spigot last summer and it bit in where nothing else would. One trick I learned: seat the jaws on the head and give the pliers a light tap with a hammer before squeezing. That pushes the teeth in past the rounded edges so they dig instead of skate. Made a huge difference on mine.

If the head is that far gone, sometimes the fastest move is just to drill it. I popped a rounded flange bolt off a tub drain last year by drilling through the head til it let go, took me about ten minutes with a 1/8 inch bit. The bolt threads stay in the bracket and you just pull the shank out with pliers once the head is off. New bolt, done. On sink hardware that's usally easier than fighting a mangled head all afternoon.

Update: went ahead and bought a pair with the front teeth. They bit in better than anything I've tried but the head is soft enough that it just kept deforming. The hammer tap trick from the second reply helped, got a little more bite that way. Now I'm leaning toward the drill method. Does the head break free cleanly, or does the shank spin loose once it's off?