Something that's last comes at the very end, after any others of its kind. The last day of the year is December 31st.
If you eat the last slice of pizza, you take the final one — it's the only one left in the take-out box. And if you catch the last plane to Bermuda, there are no more flights today. The runner who comes in last is behind everyone else, and a poet's last words are the final ones she speaks during her lifetime, before she dies. As a verb, last means "remain" or "survive."