A couple of things to note:
1. He did NOT resign. He said he would but he has yet to resign. He said he's resigning in a few weeks.
2. I don't think I heard an apology.
3. He used the opportunity to lay attacks on Trump and Moore.
4. MN Gov. Dayton is expected to appoint Tina Smith (D - MN Lt. Gov.). Whomever is the replacement, there will be an election for the seat in November 2018, after he actually resigns.