Washington ends his speech on a personal note, looking forward to what lies ahead when he retires:

Relying on its kindness in this as in other things, and actuated by that fervent love towards it, which is so natural to a man who views in it the native soil of himself and his progenitors for several generations, I anticipate with pleasing expectation that retreat in which I promise myself to realize, without alloy, the sweet enjoyment of partaking, in the midst of my fellow-citizens, the benign influence of good laws under a free government, the ever-favorite object of my heart, and the happy reward, as I trust, of our mutual cares, labors, and dangers. (50.1)

George has worked hard, and he's excited to relax on his plantation as a "reward" for all that he's done. Which seems pretty fair for the "Father of Our Country."

Washington probably closes on such a personal note because this is his official goodbye to the American people. The fact that he was president at all, and stayed on for two terms when he didn't want to, shows that he cared about the country and the people in it. That might explain why he wants to share a bit of himself and his feelings at the end.

The effect is to humanize this giant of early-American history. In the end, he's just an older gentleman (and war hero) who really wants to retire.