An AbstractClass is a class that represents abstract concepts for which objects cannot exist. (paraphrased from BjarneStroustrup)
All classes are either Abstract or Concrete. Instances of abstract classes cannot be created. Instances of concrete classes can be created.
There are generally two uses for abstract classes: interfaces, and building blocks. (concepts from Stroustrup)
Abstract classes with no implementation are useful for defining the interface to a set of classes, the "contract" between the user and implementation of some functionality. These interface classes are often found at the top of class hierarchies.
Abstract classes with some implementation are useful as building blocks, and are often found in the middle of class hierarchies. They often contain common functionality that has been pushed up from concrete classes, but they are still incomplete - they need to be derived and finished before instances of them can be created.