Currently there are only two races available within the game: Ghouls and CCG (Humans). Your race is decided by which item you choose whenever you start the game: if you eat the burger you choose to be Human/if you eat the flesh you choose to be a Ghoul. Choices are not permanent; you can have progress in both races - all you have to do is start the game and choose either the burger or meat (your progress will not be erased in either).
Along with their abilities, there are a few differences between Ghouls and CCG - Ghouls can regenerate health and deal more damage, whilst CCG have a larger supply of durability (These differences can of course be changed by increasing certain stats). The Ghoul race gains a Kagune which can be developed from accumulating RC Cells (more depth about Kagune). The CCG (Humans) have the ability to gain Quinque - weapons made from Ghoul Kagune (more depth about Quinque).