What are jiggly puffs power?

Answer 1

Jigglypuff, the pink fluffy pokemon has the ability, like its evolutions, to make the enemy fall asleep using its soft voice.

Jigglypuff has the power to also make it's trainer fall asleep if the trainer isn't careful (obviously this doesn't happen in the games).

It is actually recommended to use Jigglypuff on gym's you have trouble with, simply send the enemy to sleep then switch out Jigglypuff for a stronger pokemon and take them out.