What are Jigglypuff's strengths?

If you think Jigglypuff is slow, you're not playing her right. You need to stay off the ground as much as possible to utilize her second-best airspeed, not her last-place walking and running speeds. While in the air you can then chase, bait, and weave around opponents using five double jumps and reasonably fast aerials. Your KOs should mostly be edge-guarding and gimps rather than smash attacks and the like.

Don't overfocus on special moves like the other answer currently here does. Pound is a critical part of Jigglypuff's recovery and can be used to bust shields or tag the ends of dodges, but Rollout and Sing are highly predictable and not very useful in a 1v1 fight (often, at even medium damages, opponents you put to sleep with Sing can get up and smack you before the move is even done). Rest can't be used for surprise low-damage KOs like it can in Melee, especially against characters with high gravity and/or falling speeds, and generally is not as rewarding to land anymore. If you're playing with items, you can sometimes guarantee a KO by using Puff Up on the edge when the opponent's offstage or close to it, but this isn't trivial.