What does it mean to say "conservation of [quantity]?" Let's take the simplest example, conservation of mass. Imagine we have some closed system, say a sealed box, full of BB's only. We can somehow rearrange the BB's, shake the BB's, fracture the BB's or damage them otherwise; but no matter what we do, if the box is sealed no BB or BB part will escape. Hence, the total mass of all the BB's inside the box is conserved. Likewise, in any completely closed mechanical system mass will be conserved.
Now conservation of momentum is fairly easy to understand, also. It's basically a statement of what intuitively is inertia. That is (as Newton put it), an object in a state of motion tends to remain in that state until acted upon by an outside force. The bowling ball rolls until stopped by the pins and backstop. Similarly, the dishes stay on the table, despite the small amount of force from the tablecloth's being yanked from under them.
Energy conservation is a bit more complicated, because energy comes in so many forms. Here's an example, however. I drop a vase from a building. Initially, there is a large amount of gravitational energy in the vase, which results from my having carried it to the top of the building. After I drop it, gravitational energy rapidly becomes kinetic energy, and by the end of the fall, all of the gravitational energy I introduced by carrying it up has been converted to kinetic energy. At that point, the vase shatters, and kinetic energy is converted into the energy that breaks the vase and destroys the chemical bonds that held the vase together. Energy also goes into sound waves, heat, and the ricochet of vase pieces, perhaps even some sparks. But if you added up all the energy of the sound, heat, ricochet and chemical bond destruction, you would find that it equalled the original gravitational energy.
