This is the mating dance of the Laysan Albatross. As you can see it is a mix of head and wing movements along with trumpeting and beak clacking. I think its pretty entertaining.
The albatross are monogamous and mate for life. Only if a bird's mate dies will the albatross go in search of a new partner. The birds, once they establish a nesting site, tend to return there to nest year after year.
At this time of year, it is probably a little late to be mating and laying eggs. What's happening here is that these birds are likely younger sub-adult birds who are practicing their skills of persuasion. Probably next year these two will come back to dance, mate, and bring a new albatross chick into the world. Albatross can live for a long time. One female bird that was tagged was found returning to mate on Midway Atoll for over 50 years.
Video recorded 12-10-2006 on Midway Atoll, Sand Island