An exotic particle is a kind of theoretical particle said to exist by some areas of modern physics, and whose alleged properties are extremely unusual.
The best-known example is probably the tachyon, a theoretical particle that always travels faster than light.
Another example of this would be supersymmetry. A theoretical set of super heavy versions of known particles (this is also one of the proposed candidates for dark matter) 
Exotic particles are frequently featured in science fiction, either those with real-world academic backing, or entirely fictional.