The theory that mental states are defined by their functional roles (what they do) rather than their physical composition like in the Mind-Brain Identity Theory. A mind is like a software program on physical hardware.
Not just same outward behavior = same mind. This would be Behaviorism.
Functionalism is same inputs + internal state transitions + relations to beliefs/desires/memory + outputs = same mental state
Multiple Realizability
The thesis that the same brain states can be implemented on different systems. So both a human and an alien could feel pain but through different specific mechanisms. Humans through neurons and aliens through some alien mechanism. Forms the foundation for Computational Functionalism.