To exchange two things, with both parties giving one thing and taking another thing.
To give something else in response (where the "thing" may also be abstract, a feeling or action) To make a reciprocal gift.
I gave them apples from my tree; they reciprocated with a pie and some apple jelly.
To move backwards and forwards, like a piston.
A reciprocating engine.
To counter, retort or retaliate.
That moves backwards and forwards.