Here are a few definitions for the word: To steer away from the main topic. To take a walk on a path of topic way off from the intended one.
I remembered the word while typing the question.
Some good synonyms are Trail Off and Ramble. – lurker Dec 27 '15 at 21:09
Sometimes trail off can refer to volume, where the speaker doesn't change the subject, but just starts mumbling. – J.R.♦ Dec 27 '15 at 21:31
This may not be exactly what you were looking for, but an idiom for a long, rambling story, with many digressions, that does not really go where the listener was expecting is a shaggy dog story. – stangdon Dec 27 '15 at 23:21