Raising potential will increase the star rating of your hero, at the expense of resetting level to 1 and losing the effect of Merges. Basically starting the Hero over.
It is probably not recommended to raise the potential on a Hero you tend to use/need often unless you have enough shards to bring them back up to strength.
The benefit of raising potential is just that, the Hero will have better growth. As well as unlock new skills to use.
For example, (I'm just making up numbers) a 3 Star Corrin will have an HP of 25 at lvl 15, but Corrin raised to 4 star will get 30hp.
as to answer your question. Raise potential early if you can, that way you don't have as much work to do to bring them back up.