An interface is not a "class". That interpretation probably comes from a C++ viewpoint, whereas the closest thing to a Java Interface is a pure abstract class.
Instead of thinking in terms of abstract methods or classes, just understand that an interface defines a set of operations (or behaviors). Interface is a language construct whereby you bundle up related operations into one name.
While in Java, polymorphism and OOP relate to the actual use of Interfaces, interface is an even more general programming concept that spans various language paradigms. The main importance is to separate what a "thing" does (the interface) from how it actually does it internally (the implementation). Effectively separating the two is crucial for streamlining maintenance.