Native terrain is a creature's "home" terrain type. It gives creatures fighting in their native terrain +1 attack, +1 defense and +1 speed. Additionally, a hero moving on a terrain that causes movement penalty with only creatures native to that terrain will not suffer movement penalty. Heroes with any creatures native to another terrain will suffer movement penalty. Nomads and their native Sand terrain work differently in terms of movement penalty to other terrains.
Sieges are always fought on town's native terrain (e.g. inferno town sieges are fought on lava).