Memento = (“remember!”), imperative form of memini (“I remember”).
Mori = verb - present active infinitive of morior (I die)
memento mori = "Remember your mortality", "Remember you must die" or "Remember you will die"
When a Roman general had won a particularly spectacular victory, he was given a triumph. He would parade his army through the city itself, normally taboo in Republican Rome, and he would display the loot and slaves he had won.
He rode a chariot, and stretched out in front of him marched the senate, musicians, exotic animals, white bulls for slaughter, and captured enemies. Upon his head was a crown of laurel leaves, and all around him the populace cheered his glorious achievement.
By tradition, though, a slave rode behind him. Every once in awhile, the slave would whisper this into his ear:
Remember, you too are mortal.
Perhaps the most famous memento mori from ancient times comes from Greece, rather than Rome. It is said that a monument was placed at the pass at Thermopylae, where the 300 Spartans fended of a million Persians and saved Western Civilization. A Spartan of course was to come home with his shield or upon it; victory or death, in other words.
Inscribed in the stone was a poem which served to remind the living of this stark practice. It read:
"Go tell the Spartans, stranger passing by, that here, obedient to their laws, we lie."