I prefer not to call it "logic programming" from the point of learning the language. Too many textbooks start from explaining that "Socrates is a man" or talk about Robinson's resolution. And, as a result, student doesn't know what to do with this language.
Declarative is a vague term, but for me it means mostly a way to compactly describe your problem in domain-specific terms. There are some languages in which you can produce compact code, like APL or J. But declarative for me means readable too. And there are cases, when in Prolog one can write a more compact and readable code than in Haskell. In Prolog you can describe just the essence of the problem. Not always, of course.
Another interesting thing about Prolog that it's a small language. It means that it has only few internal parts that make it alive (The complexity of many Prolog implementations is a result of fighting for perfomance). I really like small languages (like Oberon or Forth, for example), because it's possible to learn how they work internally. And the knowledge of this inner working helps to understand the language better. There is nothing "logical" inside Prolog, just a few powerful imperative constructs.
The author of "Prolog Under the Hood An Honest Look" says:
"Prolog, billed as "logic programming", is not really. You may be disappointed if that's what you expected to find. On the other hand, having backtracking, unification, and recursion inside one computer language leads to something very powerful and special."
And I, personally, like Prolog terms very much!