In laemans terms
Pan Pan is a called telling everyone, yep there is a problem, but can handle it. Say you see your T&P's are getting a little high/low and you'd like to let people know the it's not Ops Normal.
(Read: No immediate threat to life and plane)
Mayday is telling everyone there is a problem which is endangering the aircraft and your passengers. Let's say an engine faliure.
(Read: Immediate threat to life and plane)
Of course a PanPan can be escalted to another... let's say the reason your T&P's got high/low is because you had a pending engine faliure and then your engine did fail.