In the "clipped to cycling pedals" example, the description I was recommended to aim for was "rolling a log in a circle" as opposed to pushing/pulling.
It makes a big difference to be able to have both legs "inputting" energy into the system at the same time. I would say "non-linear response" but that's probably inaccurate... but maybe not? Basically once you've overcome rolling resistance to _start_ going up a hill, being able to continue it with "both legs" instead of one feels like you're not overcoming the "zero-to-one" hurdle as much and instead staying in the "one-to-two" zone. Like you're not "starting over" every downstroke, but instead transitioning your power from one leg to the other.
Given a pretty basic commuter bike that I'd upgraded over time, it felt like moving from ~35 to ~20 tires (basic to "road bike") felt like "gaining a gear" (what used to need 1st gear, I could now do in 2nd), and same with clips, also "gaining a gear" (cumulative: now I could be in 3rd instead of being in 1st).