This new-fangled word is a variant of that other, rather better known new-fangled word, compatibility, and it means simply that something (a document, a program) written according to our specifications should work identically across different applications and different computers. "Identically" of course has to be qualified: you cannot display a document exactly the same on the screen of a handheld organizer as on a 19 inch color screen. But you can get the same experience and the same information from that document.
The issue is much clearer if you compare typical browsers: sure, they have different features, that's why people prefer one over the other, but you don't expect a page that looks blue in one browser to be red in another, or (what sometimes happens:) readable in one browser but not in another.
The developers of a specification, then, have to ensure that what they specify can be implemented by all the different implementers: it should not depend on a certain platform, it should not be open to different interpretations, and, if possible, it should be testable.
Often, when there are parts that can be interoperable and others that cannot (or only in a limited way), it make sense to split a specification into two separate ones, each with its own interoperability requirements.
For example, we don't expect that every program that can display static text documents (HTML) can also display dynamic presentations (SMIL) or vice versa, and thus HTML and SMIL are two independent modules.