The Combine Empire (or sometimes known as the Universal Union are an alien race of unknown origins that has invaded Earth a few years after the Black Mesa Accident. Earth was already damaged because of the huge swarms of Xen creatures rushing through the open portal between the two worlds, but unfortunately, the portal also acted as a very bright beacon that has been seen by The Combine Empire. The empire itself is a very powerful race that is able to invade into different universes and take over planets, draining the worlds' resources and possibly turning the critters that used to live there into slaves or Synths like Hunters and Striders.
The Combine Empire doesn't seem to be in its own control, it seems to be controlled by the Universal Union and its leaders, the Advisors.
It also doesn't seem to have perfect portal technology. The Combine technology and their military forces can be teleported into different universes, yet they cannot teleport from one place in a universe to another place in the same universe, meaning that they can only move from places on planets to other planets and between planets themselves via vehicles. That is possibly the reason of why they want to get a hold of the Borealis, an Aperture Science vessel that might contain better portal technology.