Psychonauts is set in a retro-futuristic 1980s, and follows Razputin "Raz" Aquato, an 11 year-old boy with psychic abilities, who ran away from his family's circus to sneak into Whispering Rocks Psychic Summer Camp1 to become a Psychonaut2. The series is centered on exploring the strange and imaginative minds of various characters that Raz encounters to help them overcome their fears or memories of their past.
There are 14 psychic powers in all of the Psychonauts games.
Psychonauts: Psi-Punch, Astral Projection, Psi-Blast/Marksmanship, Telekinesis, Pyrokinesis, Levitation, Clairvoyance, Shield, Invisiblity,
Psychonauts 2: All of the Psychonauts powers minus the shield, plus: time Bubble, Mental Magnet, Confusion, Mental Connection, Mental Projection.
[1] - A summer camp for children to hone their psychic powers, lead by Sasha Nein, Milla Vodello and Coach Oleander.
[2] - A Psychonaut is a spy with psychic abilities.
Information taken & paraphrased from the Wikipedia page and Mirahaze page.