Many deep-sea animals, such as corals and sponges, are sessile, meaning they spend most of their lives permanently attached to rocks. As opposed to a flat seafloor, seamounts rise off the seafloor and are basically underwater islands, providing plenty of structure for animals to attach and grow.
Also, because these animals cannot move around to find food, they are dependent upon ocean currents to bring their food to them. A seamount, rising up out of the sea floor, has strong currents that frequently run over it, providing the animals living along its flanks with a constant supply of planktonic food.
These currents also produce localized upwelling of water around the seamount. Nutrients like nitrates and phosphates, which are critical to the growth of phytoplankton, are lifted from the deep to the sunlit surface waters. These nutrients fuel an explosion of planktonic plant and animal growth, and attract larger animals such as whales, sharks, tunas, and seabirds to a veritable feast.
Additionally, those same currents carry larvae, like shipwrecked mariners, from various geographically distant areas. Seamounts thus provide a place for these lost larvae to settle and grow, so you find animals living side by side that normally are not found together.
All of these factors mean that at seamounts, you’ll likely find high biodiversity, or a wide variety of life.