A biome is a region on a planet with a certain set of features. Examples of biomes encountered in Starbound are Forest, Desert, and Ocean. While a given biome will always have the same general features, the specific characteristics of that biome can be radically different on different planets.
Forest biomes have an abundance of trees.
Desert biomes have sand.
Ocean biomes are, unsurprisingly, mostly water. Aquatic enemies spawn here frequently.
Tentacle Biomes have Tentacles in the background.
Crystal planets will have a crystalline look and feel to them.