They mainly keep your Magikarps company, but they can also boost them and cheer them on in the League.

More from my ongoing diary:

--I actually got a Shiny Magikarp on the fourth try (but it ended up as lunch for a Pidgeotto)
--Cleared the second league, and I now have a Piplup to keep my Magikarp company (he doesn't cheer like Pikachu does)
--Your Magikarp do eventually become Gyarados (but you can get Everstones to prevent this) I personally want to see what happens when a Magikarp evolves.