Pirates are the second-largest faction, most hostile ships you fight during the game will probably be Pirate Talons, unless you choose to become a Pirate yourself. Their systems and ships (if you have a B&S radar) are marked red.
At the start of the game they control three systems, each of which hosts a base: Bellamy in the Rynkel System, Munroe in TC-101 and Bounty in LV-426. Once your ship is strong enough to visit them you can buy contraband and Hidden Compartments there.
Sometimes they send out their fleets, usually consisting of a Pegasus or Nexus and a handful of fighters, to occupy neighboring systems. The Confed will usually drive them out again fairly quickly if the system was formerly one of their own. Don't worry if you happen to meet one of these pirate fleets, they will ignore the player as long as they are not attacked first, they have more important things on their minds than a single privateer.