In (Newtonian) physics, we think of things in terms of objects (which we assume are rigid, that is, they're like hard balls on a pool table and never squish or heat up or anything), forces, and position/motion.

Each object has, at any given moment, a position. That position is changing over time, and the change is called the object's velocity. And, in turn, the change in the object's velocity is called acceleration.

Changing the motion of a heavy object is harder than changing the motion of a light object. This is where we get the ideas of momentum (the velocity of an object times its mass) and of force (the acceleration of an object times its mass). Or, equivalently, you can think of force as the change in momentum over time, in the same way that acceleration is the change in velocity over time.

In the way I'm presenting it here, the definition of force gives you Newton's second law (the equation F = ma, that is, force equals mass times acceleration) for free: that's just what we mean by the word "force". It also gives you the first law: if force is zero, acceleration is zero, and therefore change in velocity is zero, too.

Newton's third law, on the other hand, says that all the forces in a system (possibly on more than one object) always add up to zero. In other words, if I apply a force +F to you, there is necessarily a force -F applied to me. If you're pushed forward, I'm pushed back. If you're pushed up, I'm pushed down. And so on.

But remember how we said earlier that one way to think of force is the change in momentum? Well, if all the forces in a system add up to zero, the total change in momentum must, therefore, also add up to zero. If you gain momentum upward, I must gain momentum downward; if you gain momentum to the right, I must also gain momentum to the left. So a modern way to describe Newton's third law is just that it describes conservation of momentum: you can never create or destroy momentum, only transfer it between objects.