I could equate it to several things, but it’s all about knowing the components.
Stand-up is a fight, if you expect to simply go into it and throw the punches you learned and it’s going to win you the match, you’ll lose. You have to take your opponent into account, learn to defend, strike and bounce back when they get hits in (hecklers, boos, and the dreaded SILENCE!).
Basically, mechanics are the components that make a joke funny, but using the components does not a funny joke make.
Take the fighting analogy, again. If you throw punches in a boxing match, you’ve used the mechanics of boxing and are a boxer, but if you throw punches in line, at the grocery store, you’re an asshole and that old woman’s family might sue.

Mechanical — just mouthing the words without the body language alignment needed for the material to be accepted by an audience as genuine. Audiences are smart and know when comedy material is simply being recited to them. That’s what mechanical means.