An alien alliance called the Covenant attacks one of Earth's outposts in the galaxy (before Halo 1) and initiate a war against humanity. In Halo 1, the last genetically modified super-soldier (Spartan II) called Master Chief discovers a ring in space called Halo. Halo 1 in centered around uncovering the secrets of Halo. In Halo 2, we learn that the Covenant have found Earth and have attacked. In this game, you fight the Covenant on Earth, as well as on a new Halo, and you also play as a Covenant alien in order to learn some back-story on them. It ends with Master Chief on his way back to Earth to locate the Ark, which is supposed to be a super-weapon. Some members of the Covenant form an alliance with the humans against a new race, the Brutes. These are supposed to be the main enemy you fight against in Halo 3.
Oh, and during all this, there is a parasite called The Flood which is unleashed and it is later discovered that the Halos were built to contain the Flood, which feeds off living things. The Ark is rumored to be located underground in Africa and is supposed to activate all the Halos, which destroy all life which the Flood feeds off of.
To answer your questions, the Forerunners are a mysterious, ancient race which built the Halos. Some people think they were humans from ancient times. There are seven Halos, and one was destroyed in Halo 1.
