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?
Interfaces will not give your code any performance boosts or anything like that, but they can go a long way toward making it maintainable. It is true that an abstract class (or even a non-abstract class) can be used to establish an interface to your code, but proper interfaces (the ones you define with the keyword and that only contain method signatures) are just plain easier to sort through and read.
That being said, I tend to use discretion when deciding whether or not to use an interface over a class. Sometimes I want default method implementations, or variables that will be common to all subclasses.
Of course, the point about multiple-interface implementation is a sound one, too. If you have a class that implements multiple interfaces, you can use an object of that class as different types in the same application.
The fact that your question is about PHP, though, makes things a bit more interesting. Typing to interfaces is still not incredibly necessary in PHP, where you can pretty much feed anything to any method, regardless of its type. You can statically type method parameters, but some of that is broken (String, I believe, causes some hiccups). Couple this with the fact that you can't type most other references, and there isn't much value in trying to force static typing in PHP (at this point). And because of that, the value of interfaces in PHP, at this point is far less than it is in more strongly-typed languages. They have the benefit of readability, but little else. Multiple-implementation isn't even beneficial, because you still have to declare the methods and give them bodies within the implementor.
The difference between using an interface and an abstract class has more to do with code organization for me, than enforcement by the language itself. I use them a lot when preparing code for other developers to work with so that they stay within the intended design patterns. Interfaces are a kind of "design by contract" whereby your code is agreeing to respond to a prescribed set of API calls that may be coming from code you do not have aceess to.
While inheritance from abstract class is a "is a" relation, that isn't always what you want, and implementing an interface is more of a "acts like a" relation. This difference can be quite significant in certain contexts.
For example, let us say you have an abstract class Account from which many other classes extend (types of accounts and so forth). It has a particular set of methods that are only applicable to that type group. However, some of these account subclasses implement Versionable, or Listable, or Editable so that they can be thrown into controllers that expect to use those APIs. The controller does not care what type of object it is
By contrast, I can also create an object that does not extend from Account, say a User abstract class, and still implement Listable and Editable, but not Versionable, which doesn't make sense here.
In this way, I am saying that FooUser subclass is NOT an account, but DOES act like an Editable object. Likewise BarAccount extends from Account, but is not a User subclass, but implements Editable, Listable and also Versionable.
Adding all of these APIs for Editable, Listable and Versionable into the abstract classes itself would not only be cluttered and ugly, but would either duplicate the common interfaces in Account and User, or force my User object to implement Versionable, probably just to throw an exception.