Lot's of good info so far. It looks to me like the clutch was slipping and overheated. Could be caused by a dull chain and/or pushing the saw too hard in the cut. Keep the RPMs up, try leading with the tip of the bar forward, cutting at a slight angle.
Hope this all works out for you, it's a great learning experience.
Hope this all works out for you, it's a great learning experience.