Plain English Meaning
Squirting a small amount of fuel into the engine before you try to start it, so there's something ready to burn the moment the engine turns over.
Full Definition
The act of injecting a small amount of fuel directly into the engine's intake or cylinders before starting, to provide an immediately combustible fuel-air mixture that allows the engine to fire and run on its first cranks. Priming is typically performed using a manual primer pump or, in fuel-injected engines, by briefly running the electric boost pump with the mixture rich. The amount of priming required varies with engine temperature -- cold engines need more, warm engines need little or none.