It means to say something suddenly and without thinking, often because you are nervous or excited.
For example:
* "He blurted out the answer before I could stop him."
While there is a noun form of "blurt", it is rarely used. It would refer to a sudden, unplanned utterance. For example:
* "His confession was a blurt of emotion."
However, it's much more common to use "blurt" as a verb.