Dramatic poetry is a play that uses poetic language. The most famous writer of dramatic poetry is, of course, Shakespeare, who wrote four types: tragedy, comedy, history, and romance (tragi-comedy).
Depending of the play, Shakespeare's plays were about 75% poetry and 25% prose. Of the poetry, he used two types of verse in his dramas: rhymed and unrhymed. More than 75% of his dramatic verse was unrhymed (blank verse).
There are other dramatic poems: the closet dramas (poetic plays that were never intended to be staged). Of these, Byron's Manfred and Milton's Samson Agonistes are chief. Not all closet dramas are poetic, of course, but if it's written by a poet, it most likely is.