Momentum is a second great conserved quantity, and it is the key to understanding collisions, recoil, and rockets. Where energy is a scalar amount, momentum has a direction, and that makes it especially good at describing what happens when things hit.
What momentum is
The momentum of an object is its mass times its velocity:
It measures how much motion a thing carries and how hard it is to stop. A slow-moving truck and a fast bullet can have similar momentum by very different routes: great mass and small speed, or small mass and great speed. Because velocity has a direction, so does momentum.
Conservation of momentum
The central law is that the total momentum of an isolated system does not change. This follows straight from Newton's third law: in any interaction the forces on the two bodies are equal and opposite, so whatever momentum one gains, the other loses, and the total is untouched. No outside force, no change in total momentum.
Collisions
This makes collisions solvable. When two objects crash, their individual momenta change wildly, but the sum before equals the sum after. Two billiard balls, two cars, two subatomic particles: add up the momentum going in and it must match the momentum coming out. In an elastic collision kinetic energy is also conserved and the objects bounce cleanly; in an inelastic one some energy becomes heat and deformation, and they may stick together, but momentum is conserved either way.
Recoil and rockets
Conservation of momentum also explains recoil. A gun and its bullet start with zero total momentum; when the bullet flies forward, the gun must move backward so the total stays zero. A rocket works the same way on a grand scale: it hurls exhaust gases out behind it, and to keep the total momentum balanced, it is pushed forward, which is how a rocket accelerates in the vacuum of space, with nothing to push against but the stuff it throws away.