Partial power outage upstairs
It just means that a wire termination (where a wire meets a receptacle, wire nut or switch) failed somewhere from the overload.  It failed in an arc-fault mode, meaning it burned out like a fuse then arced across the gap, until the arc self-extinguished.  If it had not, you'd be seeing your insurance man in the morning. 

The connection didn't short against another wire, so it didn't make a short circuit. That's why it didn't trip the breaker.  Breakers are not "Magic Master Detect-All's".  They make those; they're called dual-mode AFCI/GFCI breakers.  The AFCI would have tripped from the arcing, stopping the arc in case it did not self-extinguish. 

So now you need to go hunt down the bad connection, starting at the panel.  Electrical circuits are wired like a tree, they can have any number of branches, but they never loop back to themselves.  Most are wired linear like a vine.  The problem is either at the last functioning outlet or the first bad outlet.  The top candidates are: 


Backstab connections
Aluminum wire on old non-aluminum-rated terminations (basically all terminations out there on Al wire) 
Loose amateur-done wirenuts - wirenuts are one of the few times "gorilla tight" is appropriate
Screws not tightened enough