Have you ever played with a water squirt gun? When you squeeze the trigger, the water shoots out and the gun sometimes kicks back a little bit. That's because the water coming out creates a force pushing the gun in the opposite direction.
A recoilless rifle is a big gun that shoots much more powerful things than water, like rockets or grenade launchers. When it fires, it also creates a force pushing the gun in the opposite direction, just like the water gun example. But recoilless rifles are designed to get rid of that force, so the shooter doesn't get knocked over or hurt.
How do they do that? Well, inside the gun, there are two tubes. One tube holds the ammunition and the other tube has exhaust vents on the back. When the gun fires, fuel and air are mixed together and ignited, creating a big burst of hot gas which shoots out the back of the exhaust vents.
That burst of gas pushes against the air outside the gun, and the reaction to that push is what would normally cause the gun to recoil. But in a recoilless rifle, that hot gas is also shooting out the back of the second tube. This creates a secondary force that moves in the opposite direction of the first force, canceling it out.
So, in simple terms, a recoilless rifle is like a big squirt gun that shoots powerful things and doesn't kick back very much so the shooter doesn't get hurt.