The Cosmic Toads appeared to help Mario on his journey, teaching him how to use Launch Stars (or Boost Stars), his new moves, and helping him as much as possible. They are often seen with Space Rabbits. In fact, some videos seemed to show a Space Rabbit turn into a Cosmic Toad. Therefore, (at least some, if not all) Space Rabbits were really Cosmic Toads.
They also generously give Mario Star Shards when they see him, though Mario has to help them with numerous things as well. The Cosmic Toads look similar to regular Toads, though they have several changes, such as their Mushroom heads have stars instead of dots on them, they wear oxygen helmets (so it seems), and their heads are somewhat thinner and taller.
In the final version of the game, they appear to be replaced by Lumas.
While no basic Cosmic Toads have actually appeared in actual games to date, the Starshade Bros. from Mario & Luigi: Superstar Saga and it's remake are very likely Cosmic Toads, as they wear helmets (as it looks), have starred mushroom caps, and are somewhat taller than the other toads in the game. Not to mention the fact that they are found in Stardust Fields.