First of all, there's difference between OOP paradigm and OOP implementation in Java, so same words may mean a bit different things.
In OOP the paradigm interface is what you can do with the object (or what object can do for you). Any object can have several interfaces and thus play different roles. For example, someone may work as a programmer and be able to create programs, but at the same time he may be a husband and father and thus be able to pay the bills for his family and take care of children. Here "programmer", "husband" and "father" are interfaces, and a person is an object that implements them. Note, that interfaces do not imply presence of any specific features (fields) for implementing object, just actions that this object should be able to perform.
Java more or less follows this idea, but as any paradigm implementation has its own features. Java allows describing methods, that is actions that the implementing object should be able to perform, but not any implementation details, thus, nothing about object fields or private methods.
But what about constants (
public final static fields)? Are they part of implementation or interface. It could be both. E.g. interface "programmer" can have constant
WORK_HOURS set to "8". Thus Java allows you to describe constants in interfaces too.
Note, that Java only helps you to make good OOP design, but it doesn't strongly require it. In particular, not all public methods of an object should exist in interface too. For example, getter and setter methods are normally public, but in fact they are the part of implementation, not interface, and thus it's worth not to bring them into interface.