In all of my music education these last several years, the term I've learned that has proven most helpful is rubato. When it appears on a page of music, it signifies the freedom of rhythmic flexibility. One music dictionary defines rubato as meaning not strictly on the beat, and any notation that lets me miss that often elusive pulse is just fine with me.
Literally, the Italian word translates as stolen or robbed, as in stolen time. In music, you can steal time from a measure in order to express a certain emotion.
I don't often use this notation with my horn playing because most of that is done in a group setting, although I have tried to get away with it in lessons. Try being free with the tempo while other people are playing with you and see how happy they are about the time you've stolen from them.
It's actually when I sit down at the piano that I find "rubato" most helpful.
I use the technique freely when I play regardless of the music at hand. I say that I get to take my time on the hard stuff and speed up on the easier stuff. I interpret the term to mean I can start out at the beginning of a piece with the suggested tempo but take off from there and end up where ever I darn well please. And when I stumble on a complicated five-note chord I have forgotten to prepare for, I can take my time to get all the notes regardless of the noise coming from the metronome.
It's sort of like claiming sanctuary in a church. If you play at varying tempos or unevenly within a measure, you simply shrug and say "rubato," and you're immediately protected from criticism. Plenty of people will accuse me of abusing this very freeing term, of stealing time inappropriately, but as I only play the piano for my own amusement (and occasionally for your horror), I call sanctuary.
Here is a piece I love to play—a Chopin nocturne—and I use rubato throughout because I play it so poorly. It's allowed one time at the top of the last page, but I need to steal time in a variety of places. This particular recording is foul with Tiger laying on the laptop halfway through and my giggling at some of the worst of my playing. I apologize for not offering a cleaner recording, but I'm sticking with my plan to only post first attempts.