In a normal rifle, the barrel lies at the very front of the gun, with the firearm action (or mechanism) behind that, and finally the stock at the extreme rear. The trigger is best located directly under the mechanism, which "forces" the magazine to be placed in front of it to be out of the way.
In the bullpup configuation the magazine is instead located behind the trigger, which allows the entire mechanism to be moved rearward. The trigger now operates through a small pushrod system (or something similar), which has the disadvantage of being less reliable. On the upside the magazine can be placed right within the stock, cutting the length of the weapon some 20%.
Bullpup weapons have been the subject of some debate. Mechanisms typically ejects casings to the side, this means that the typical bullpup design must be fired from only one side of the body, or the casings will hit the operator in the face. Some weapons have allowed the ejection to be switched by re-assembling it, but this is hardly a reasonable solution in battle.