Copper weight/thickness current capacity
I can't speak to your specific requirements but I can say that I designed a board with 8 mil traces that carried VCC @ 12V. While testing the board I accidentally shorted the trace to ground and had the board delaminate - literally the traces turned black and burned off the board. It took a while to figure out what on earth was going on because as soon as a small bit burned it acted as a fuse.

So, that's what happens when too much current goes through a trace - it melts.