How does work relate to conservation of energy?
Work is said to be done when a force acting on some object causes a change in the objects position or deforms it.
That's not the end of the story! Every time that work is done, there automatically is a change in the energies of the system(that is, energy is converted from one form to another)
It becomes really intuitive when you think about it for a sec! When a force is applied to an object in motion, the object will either slow down or stop or move faster. This shows us that kinetic energy is either gained or lost.
Consider a case where two cars collide, work is done, by each car on the other to deform, and alter the position or direction of motion of the other.
This work is accompanied by sound, heat and kinetic energy changes. Showing that by all means energy is conserved.
Another way to look at it is: "every time work is done, there must be some energy changes, because the energy of that system must be conserved"