Suspend is a term for pausing a computer during execution. It usually involves stopping execution of the processor and storing everything in RAM or on the hard drive. Implementations differ.
It is typically used for laptops where the user suspends the computer while they move from place to place. This saves the user from having to start and stop the machine etc.
Linux's support for suspending a machine is getting better but is still often flaky. It isn't helped by laptop's often having buggy or badly implemented power management (which helps in this matter).