Recoil is the force pushing the gun back when the ammo goes forward out of it. The momentum of the ammo is exactly equal to the momentum of recoil, in the opposite direction. Momentum is mass times velocity, so a small, light piece of ammo moving very fast equates to a big, heavy object (like a gun and the person/thing holding it) moving much slower (as in, not supersonic and you can actually see the movement).
Recoil is why you can injure your hands or wrists by firing a hand-held gun that isn't properly aligned (and braced against your shoulder if it's a long gun), and why you see the gun, hand, and arm all jerking back and up with each shot, and why it feels like the gun just punched or kicked you in the hand/wrist/shoulder after you've fired.
It also applies to bigger guns. An A-10, an American attack plane, fires such heavy bullets at such a high rate that its recoil exceeds the maximum power of one of its jet engines, so the engines have to increase thrust while the gun's firing, just to maintain the plane's speed. The only way to put a bigger gun (or more of them) on a plane and still have the plane be able to fly while firing it is to use a modified cargo plane like a C-130, because its greater mass makes it harder to push around. A battleship's big guns' recoil rolls the whole ship a bit, and would sink most smaller ships if they foolishly had such a gun mounted on them and foolishly fired it.
And if you watch a video of a tank firing its main gun, you'll see the whole tank bounce and rock due to the recoil.
Now here's the catch: anything sitting on the ground is deceptive about recoil because it directs most of the force into the ground. That way, the momentum mostly goes into moving the Earth instead... by an immeasruably tiny amount, because the Earth is so much more massive. If all of the momentum of recoil went into moving the gun and gun-holder, they'd go falling back out of control much farther and faster. And that's the situation a tank would be in if it were hovering: its own gun would keep pushing it around each time it's fired, away from whatever its target was.