Jumping is a graphical glitch in PokeMMO.
A player is seen to jump when they walk over a game object that is there to the observer, but not to the 'jumping' player. For example, if a player removes a small tree with Cut and walks through the gap, he or she will appear to 'jump' for players who have not removed the tree. A similar situation can occur for NPCs that are still there for the observer, but not for the jumping player.
Due to the nature of the glitch, players will never see their own character 'jump'.
In player culture
Jumpeon and the Jump Stone
A common (and deliberately misleading) response to "How do I jump?" is that one must use a Jump Stone on Eevee to obtain Jumpeon, which would allow players to jump by using a move of the same name. Both Jumpeon and the Jump Stone are fictional and do not exist in PokeMMO or the official Pokémon games, and represent early examples of in-jokes among the PokeMMO community.