Interfaces allow you to create code which defines the methods of classes that implement it. You cannot however add any code to those methods.
Abstract classes allow you to do the same thing, along with adding code to the method.
Now if you can achieve the same goal with abstract classes, why do we even need the concept of interfaces?
I've been told that it has to do with OO theory from C++ to Java, which is what PHP's OO stuff is based on. Is the concept useful in Java but not in PHP? Is it just a way to keep from having placeholders littered in the abstract class? Am I missing something?
The entire point of interfaces is to give you the flexibility to have your class be forced to implement multiple interfaces, but still not allow multiple inheritance. The issues with inheriting from multiple classes are many and varied and the wikipedia page on it sums them up pretty well.
Interfaces are a compromise. Most of the problems with multiple inheritance don't apply to abstract base classes, so most modern languages these days disable multiple inheritance yet call abstract base classes interfaces and allows a class to "implement" as many of those as they want.
The concept is useful all around in object oriented programming. To me I think of an interface as a contract. So long my class and your class agree on this method signature contract we can "interface". As for abstract classes those I see as more of base classes that stub out some methods and I need to fill in the details.