Dipping hand into liquid nitrogen
What happened in the video above is that there is a formation of an insulating gas barrier between the liquid nitrogen and the “relatively hot” hand. The gas barrier slows the heat transfer from the hand to the liquid nitrogen, allowing the hand to escape unscathed after being dipped into liquid nitrogen.
For the drops on the frying pan, the bottom part of the water droplets vaporizes immediately when it comes into contact with the hot frying pan. This forms an insulating gas layer that slows down the heat transfer from the pan to the water droplets. This allows the water droplet to “sit” on top of the air layer.
Another version of the Leidenfrost Effect: