To me, in a declarative programming language you tell the computer what you want without exactly telling it how to achieve it. It's the compiler's job to figure that out. That classic example of a declarative programming language is Prolog.

In databases there are two traditional approaches to extracting queries: the relational algebra and the relational calculus. One of these (the relational calculus) is very clearly declarative: you essentially are saying "give me all students whose ID numbers are less than 1000 and who took a class from someone who is no longer a member of the faculty." The interpreter figures how what relational operations should be performed to do this.

The other option is the relational algebra, which to me is very obviously not declarative: you are telling the system exactly what to do, and giving it an implicit ordering (though just like in any procedural language it can change the ordering if it thinks it's a good idea). Thus in the relational algebra you'd say "get the table of students. Reduce it to those whose ID numbers are less than 1000. Join it with those students who took a class. Take the list of faculty. Reduce it to those who are longer teaching. Join that with the previously generated students relation. Project out just the student names."

The primary language for the declarative relational calculus is Datalog.

The primary language for the (non-declarative) relational algebra is SQL. Though SQL has a few extra gizmos added to compensate for the fact that it's less expressive than the relational calculus.