Map Savestates
Explanation
Every time and no matter how you leave a map, information about your time playing it will be saved. This contains things like your position, potion effects, stats, etc. If you reset your progress in a map, your player state information will also be deleted.
Completing a Map
Upon finishing a map, you will receive a diamond helmet and be able to fly around. Furthermore, your now completed savestate will be recorded and categorized, and you will be able to see it, as well as compare it to your best run (shortest completion time). Rejoining the same map after this will start a new savestate for you.
Spectator Mode
At any time while playing a map, you can switch into spectator mode. When in spectator mode, your play-time will be paused, and you will be allowed to fly and move freely around the map. In your hotbar, you will also receive several useful items that allow you to set and return to artificial checkpoints, toggle your flight, and teleport to other people to watch them play.
You can enter spectator mode right-clicking the middle item in your hotbar, or by using the /spec command.