Tropical climates are a lot closer to the equator than temperate climates. As you probably know, the equator gets the largest amount of sunlight per year; as a result, more plants can grow there...
Algae is (are) the most prevalent plant in the ocean. Indeed, the ONLY plant in the ocean. Seaweed, kelp, etc. are all different forms of algae. There are no rooted plants like we see on land, though...