The burden of Nineveh - משא massa not only signifies a burden, but also a thing lifted up, pronounced, or proclaimed; also a message. It is used by the prophets to signify the revelation which they have received from God to deliver to any particular people: the oracle - the prophecy. Here it signifies the declaration from God relative to the overthrow of Nineveh, and the commission of the prophet to deliver it.
As the Assyrians under Pul, Tiglath-pileser, and Shalmaneser, three of their kinds, had been employed by a just God for the chastisement of his disobedient people; the end being now accomplished by them, God is about to burn the rod wherewith he corrected Israel; and Nineveh, the capital of the Assyrian empire, is to be destroyed. This prediction appears to have been accomplished a short time after this by Nebuchadnezzar and Cyaxares, the Ahasuerus of Scripture.
Nahum, נחום Nachum, signifies comforter. The name was very suitable, as he was sent to comfort the people, by showing them that God was about to destroy their adversaries.