MESSENGER means the one sent with the message — a forerunner of God's message (The New International Webster's Pocket Dictionary of the English Language).
The term 'God's Last Messenger' refers to the person whom God will anoint to carry out His last mission of Salvation. And why the Last Messenger? Per the Holy Scripture's description, the current works of salvation will be done until Judgment Day. And, on Judgement Day, it was prophesied that the current world and those up in the sky would all perish, thus, the current dealings in our lives are being done in these last days.