Here's a set of videos on work and energy (9min, 9min, 10min): Khan Academy: Introduction to work and energy, on YouTube, Khan Academy: Work and Energy (Part 2), on YouTube, Khan Academy: Conservation of Energy, on YouTube
This video from the First Law section is also about work and heat (13min): Khan Academy: Work from Expansion, on YouTube
In physics, work is defined as motion over some distance against an opposing force. (A force is an acceleration multiplied by a mass.) For instance, lifting an object against the force of gravity. The amount of work is the opposing force multiplied by the distance the object moved. The amount of work done in lifting an object is the force of gravity (the mass of the object times the acceleration of gravity) times the height you lifted it. There are lots of other ways systems can do work: a stretched spring can expand and lift a weight, a battery or burning gas can drive a motor and move a car up hill or forward against friction and wind.
In chemistry, work is often defined in terms of a change in volume
against a pressure. (Pressure is force divided by area, so convince
yourself that P x V has the same units as F x d). For instance,
atmospheric pressure is constant at ~1 atm. If you have a sample of
gas at higher pressure, and you let it come to mechanical
equilibrium with the atmosphere, it will expand to some new volume. The work it does
expanding against atmospheric pressure is (1 atm)(ΔV), where
ΔV is the final volume - initial volume. In general, the work
done by gases expanding is called pV work, and is
w = ∫ p dV
For our purposes, we won't be dealing with integrals, so we won't
calculate work this way unless the pressure is constant, in which
case we can use the simpler equation
w = - PΔV
where P is the constant pressure and ΔV is the change in volume
of the system. The negative sign accounts
for the fact that if the system is compressed, ΔV is negative, and
work was done to the system, so w is positive.
There are several different definitions of heat. For instance, we can heat water to make tea, or enjoy the heat when we enter a warm room in the winter. In thermodynamics the meaning of heat is more precise: it is a process, a way energy can move. Heat is energy that moves from a hot object to a cold object. When heat leaves the system, it has a negative sign, and when it enters the system, it has a positive sign.
Heat and work are the ways that energy can move between objects. When you think about the molecules, the difference between work and heat is very simple. Work involves an orderly motion of molecules, like all the molecules in an object moving the same direction. Heat involves disorderly or random motions of molecules.