Due to the barrier of vapour, the water droplet essentially floats or "levitates" on a cushion of water vapour. This is why the drop does not spread out on the hot surface and retains its shape for a short time. The water droplet may even bounce around in the vessel as it bounces on the layer of water vapour.
During this process, the water vapour rapidly expand and push air around the water droplet. The collision between the expanding water vapour and air molecules causes the sound waves that we hear as the sizzling or popping sound. The sound is also influenced by the size of the water droplet, the heat of the vessel, and the properties of the liquid.
As more and more water droplet fall into the vessel, they join together and eventually form a continuous layer of vapour underneath the entire body of water. Once this happens, the popping sound subsides and the water begin to boil and evaporate in the more usual way.
The Leidenfrost effect is not just limited to water, but can also occur with other liquids depending on their boiling point and the temperature of the hot surface.