What is the function of a flywheel in a machine?

You might want to be specific in what you mean by machine eg, lawn mower, car engine, motorcyle engine, steam engine etc. However, generally flywheels are there to create rotating inertia. In a car engine, energy is used from its rotating inertia to move all the strokes apart from the bang or power stroke. Energy is the then put back into it when another power stroke happens.

From this you can see that it also helps to keep a constant rpm in an engine. If not the engine will hop all over the place especially at low rotation speeds. According to my own theory, it develops gyroscopic properties above a certain rotational speed; this will steady the engine (basically reduces resonance dramatically). In a motorcyle with a very heavy flywheel, there might be problems cornering it due the gyroscopic effect. Again this is my theory.

The flywheel might have some functional surfaces. For example gears that mate with that of starters (either manual or motor) to kick start fast enough power strokes from no rotation. Also, it can house magnets that rotate with the flywheel around coils to induce emf for power generation. Some manufacturers use keys to lock the flywheel and the crank shaft because the flywheel might be involved in the spark system.

Be specific next time, I could probably go on if there were specifics. You can do some research on inertia and newtons first law. Excuse my English as well...