There are basically two cursepert sets you're likely to see. The first is offensive -- three attacks and curse as the last move with substantial specially offensive investment. In that case, the pert uses curse to exert pressure on mons it wouldn't be able to otherwise -- namely, Blissey and defensive Starmie. The later would normally be able to spin on Pert for free but it can't spin for free if it enters on Curse. It gives Pert a way to go toe to toe with Snorlax, too. The Swampert often ends up luring Skarmory attempting to Phaze it, which it can chunk with pump -- the same is true of defensive Zapdos. You'd probably pair this with a second rock resist.What's CursePert's niche over the other standard Swampert sets? The smogon dex entry only lists it as a footnote but I've seen it pop up a few times in competition and was wondering what teams benefit from it.
The second is defensive. This one has rest, usually rest IB curse EQ, but sometimes they have slide instead of beam. This set would only be used on teams featuring Magneton, and it would only be used on slow variants of those teams, probably with their own Spikes. In this case, the pert has all the defensive utility of a regular pert -- checking DDers, Aerodactyl, and Metagross -- but it also gives an auxilary win condition against certain slow builds. For example, Skarm + Dol + Milo + Bliss + Dug has no way to disrupt cursepert once Skarmory goes down. Forretress + Tyranitar + Blissey + Pert is forced to trade their own Pert to take defensive cursepert out, which is a trade that Pert's teammates might be able to exploit. It can force certain variants of Snorlax and Metagross to blow up to take it out, too. And it does all this while being a Swampert meaning that the team its on will be far safer against some of the most dangerous threats in the game should the matchup be offensive. This set is usually paired with Wish or Aromatherapy.