Jerry is a very small, realistic looking snail. In the episode, "Dumped," SpongeBob compared him to Gary the Snail and Lary the Snail, saying, "And Gary and Lary are really different than... Jerry." and then took him out of his pocket. He has no voice actor.
Jerry closely resembles the snail species known as Helix pomatia, also known as the edible snail, burgandy snail, or the roman snail.
It is unknown if Jerry is SpongeBob's pet or not because he's not feeding him or anything.