EGT tells you were you are relative to the thermal limits of the engine. You can start doing bad thing at ~1,700dF. I've seen turbine wheels actually crystalize and explode at just over 2,000dF.
Peak EGT occurs at Stoich..
Rich or lean of stoich drops the temps..
It's generally just considered safe to add fuel if you're getting too hot, but it's not a real good AFR guage.
Retarded timing can also drive up EGTs.
EGTs, a WB, a stop watch, and reading plugs is what it takes to dial in a tune correctly.