Mechanic
Also said as Game mechanic
A verb together with the rules that answer it: what you do, and what the game does back. Double jump is a mechanic: the verb is jump, and the rule is that you may do it once more in the air.
It is the smallest piece of a design you can add, remove or argue about. Saying which mechanic you mean stops vague talk about "more gameplay".
Say it
“Keep the jump button, and change the mechanic: touching a wall counts as ground, and jumping off it sends you the other way at 300 px/s.”
Where you’ve seen it
Portal's central mechanic is two linked holes, along with the rule that your speed comes through with you. The verb is only "shoot", and the rule is what makes it a puzzle.
Not to be confused with verb
A verb is the action. Two games can share the verb jump and have very different mechanics, because the rules behind it differ.