A Bullpup is simply a rifle where the action (i.e. the area of the receiver where the bolt, magazine, and barrel all meet) is located behind the firing grip instead of in front of it.
In a traditional layout rifle, such as the AR-15, the action of the weapon is in front of the grip and trigger. All the area behind the grip is "wasted space" and usually ends up as a buttstock with adjustment or storage.
The advantage to the "bullpup" layout and design is that you can get the same length of barrel in a much shorter overall length. In the picture above, the AR-15 and the Steyr AUG both fire .223 caliber ammunition from the same type magazine and both have a 16" barrel, but the bullpup layout allows the Steyr AUG to be considerably shorter and handier.
Bullpup rifles are gaining more and more adopters every day, and Bullpup Shoot 2015 is meant to bring together those who appreciate the advantages of this style of rifle!