One can say that energy is a concept similar to work. Both concepts
are mathematically defined. In many situations work is F*x, where x is
a displacement and F can be many different things, such as m*g
(gravitational force), k*x/2 (Hookean spring force), etc. Then the
concept of kinetic and mechanical energy can be introduced.
Some mathematically defined quantities turned out to be very useful.
In my teaching this was strongly emphasized in solving inclined plane
problems (without considering friction and air resistance). The
terminal velocity obtained from the law of conservation of energy
turns out to be the same as by using the concept of acceleration.
I agree with JohnD; energy should not be defined as "ability to do
work." But there is nothing wrong, in my opinion, with saying that it
is a concept similar to work. That is how I would now introduce it in
a very first physics course. The unit of energy and the unit of work,
by the way, are identical.
Ludwik Kowalski, a retired physisist
5 Horizon Road, apt.2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/