When you recoil, or recoil from something, you pull yourself back, away from whatever it is that scares you or disgusts you.
For example, if I see a snake, I'll recoil. Recoiling from the snake is what my body does automatically—it happens really fast, without me thinking about it.
You might recoil from a roach, or recoil from a hunk of rotten cheese, or recoil from a stranger who's trying to get all up in your personal space, or recoil from a friend who's trying to kiss you when you don't want them to.
You can even recoil from ugly sounds or terrible ideas. Many people recoil from the sound of fingernails on a chalkboard. (Eugh!) I'd recoil if you said, "Do you dare me to eat a whole onion raw? I'm gonna do it."
Recoiling is usually something people do, but objects, too, can recoil. If someone fires a weapon, it might recoil, or kick back against that person. Which is an excellent reason (among many others) to not fire a weapon!
By the way, "recoil" can also be a noun. We talk about a weapon's recoil—how strongly it kicks back against the person who wields it.
Lastly, I bet you know something about the prefix "re-," which is that it often means "back" or "again." And so you may be guessing, does "recoil" literally mean "to coil back, or to coil backward, like a ribbon"?
While that's an excellent guess, nope. "Recoil" isn't based on the word "coil;" it's based on the Latin culus, meaning "the bottom, the backside"—yup, the butt! So, "recoil" kind of more literally means "to back up, to go backward, or to go behind." Perhaps butt-first, like this cat.