Plain English Meaning
A little pump in the cockpit that squirts a small amount of fuel straight into the engine to help it start, especially when it is cold.
Full Definition
A small hand-operated pump that draws fuel from the tank and delivers it directly into the intake ports of the engine cylinders or into the intake manifold, used to aid starting — particularly in cold weather when the engine is hard to start.
Context Anchor
You encounter the fuel primer during engine starting procedures, especially in cold weather or after the aircraft has been sitting.
Derivation
From the verb 'to prime,' meaning to prepare something for action by supplying it with what it needs to begin working — the same sense as priming a water pump. The primer 'primes' the engine with fuel before the start.