in-: in, into
spect: derived from Latin "specere", meaning "look"
-ion: the action of doing something
So inspection means:
The action of looking into something.
If someone wants to look into something, the first step is to open it. This action is always from an official whose job is to examine that something meets rules. So, inspection means "examination".
Evolution of usage
The action of looking into luggages is necessary in airport.
The action of inspecting luggages is necessary in airport.
The inspection is necessary in airport.