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.