After the blessings are said the shamash is lit and the first Hanukkah candle (the one you placed in the rightmost position of your menorah) is kindled using the flame from the shamash. Place the shamash in its place on your menorah. (Usually there will be a special spot for it in the middle of your menorah.)
You allow the shamash candle to burn. If this is what I think it is, what he is doing is what I do. I hold the shamash over the holder to drip hot was into the cup so the candle stands up straight and does not loosen and fall over.
In fact, with my menorah, I do it with every candle.
wax