The Tyranids are an extra-galactic swarm of aliens who invade driven by a neverending hunger to consume all in they're path. They are ever evolving, and use this to they're advantage when dealing with enemies that require them to use different types of evolutionary bio-morphs to better fight them.
They are controlled by an entity known as the Hive Mind. This being is the intelligence and will of the entire Tyranid Race. Vassals of the Hive Mind are Synapse creatures who control the smaller creatures. The larger they are, the more Tyranids they control. The major controllers are beings known as the Hive Tyrants, who act as generals during Tyranid Invasions.
Their method of space travel are through the use of gigantic bio-constructs known as hive ships, which then form into hive fleets, which contain countless billions of Tyranids. However, it is theorized that these hive fleets, enormous as they are, are merely scouting vessels for even more gigantic fleets.
What is frightening about the Tyranids is that their full origins are a mystery. It is presumed that they have already consumed one if not more Galaxies, and the Milkyway Galaxy is their latest. Another theory is that they are fleeing from something even greater a threat than them.