A valediction is a goodbye — but a formal, prepared one, especially the speech you make when you are leaving. When a professor retires and gives a last lecture, or a leader steps down and speaks to the nation one final time, that is a valediction. The word carries weight and ceremony; it is not for waving to your friend at the MRT station.

There is a second, quieter use that is actually more common in daily life, though most people never learn its name: in a letter or an email, the valediction is the closing line before your name — 'Sincerely', 'Best regards', 'Yours faithfully'. Teachers of writing use the word this way all the time. So the word covers both ends of the same idea: the formal spoken farewell, and the little written farewell at the bottom of a message. It is a rather bookish word either way, and you will read it far more often than you will say it. The adjective is 'valedictory'.