PSPACE and NP complexity
NP is a complexity class with constraints on time, whilst PSPACE is a complexity class with constraints on space.
The difference between time and space is (in this case) simple: Space can be reused, whilst Time cannot. A Space-bounded machine can run for as long as it wants (as long as it terminates).

Therefore we can construct a PSPACE-Machine that solves SAT: The machine simply tries every solution.