An abstract class is simply a class that can't be instantiated. It can have anything a normal class can have (fields, non-abstract methods, etc.), as well as can have abstract methods. Most often this is done to provide a class which has some implementation of a class, but not all of it.
ex.: A car class could implement that you steer by turning the wheel, but how it turns would be implemented by inheriting classes.
If you want a "class" with only abstract members (aka purely abstract class), you could create an abstract class, or you can create an interface. The interface is an abstract class which has and only abstract methods (static methods/fields are ok, though).