To force an egg is when one attempts to make an egg hatch earlier by using the kill action on it. This sometimes results in the egg breaking and releasing a hatchling. It can only be done when the egg has low time, and a very large hole, or it will almost certainly fail.
Even then, it is not advisable. If the action fails, you will be left with a dead egg on your scroll for 2 weeks. This egg will also take up one of your slots for 24 hours after killing it. Even if the forcing is successful, the hatchling might be so scared that it will run away to the AP.
Another method of forcing is the Earthquake breed-specific action.