I think you misunderstand what an abstract class is. Abstract classes cannot directly be implemented (i.e. you cannot call new AbstractClass()). They must be extended to be used.
The idea behind having one is that you may have a concept of, say a Cat, and you have different species of cats.
What you could do is create an interface called Cat and then implement it a number of times to create your different species. This is perfectly acceptable, however as the number of cat species increases this starts becoming more and more unwieldy as you have to implement all methods each time a new species it added so you may end up repeating a lot of code.
One solution would be to create a GenericCat class to hold all the the common code and methods, and then extend this for each of your species, overriding the methods for each species as needed. This poses two problems though. Firstly it allows for the GenericCat to be implemented directly, which we don't want any one to do, and secondly we have to implement all the methods defined in the interface, meaning that when we create our new species we may forget to override one of the methods that we need to, thus introducing a possible error.
A better solution would be to use an AbstractCat class that implements Cat and then only implements the methods that will be common to all Cats.
That way we don't have to worry about developers trying to directly implement AbstractCat(i) as there will be a compile error, or if they forget to implement a method as again this will cause a compile time error. It also means that the code will be cleaner as the abstract class will not be cluttered with empty methods or ones that return arbitrary values (which should also help reduce the risk of error).
(i) Note: I am telling a bit of a white lie at this point as developers can sort of implement AbstractCat, but as it confuses matters I thought I'd leave out the fringe cases. For more info though have a look into Anonymous classes and possibly the use of Reflection.
I hope I haven't confused matters too much :-)