This phrase tells how long something happened up until now. In positive sentences, it means that something continued from the time specified until now:
I was in Boston for the last 3 days.
In negative sentences, it means that something did not happen during that time:
We haven't eaten anything for the last 8 hours.
You can say a specific number, or use a general word like "few" or "several":
She hasn't heard from him in the last several days.