In the movie, the United States Air Force comes into possession of a piece of alien technology known as the Stargate, a large ring-shaped device which uses wormholes to transport people instantaneously across the universe to other planets. With the help of archeologist/linguist Dr. Daniel Jackson, the USAF learns how to activate and use the Stargate. A mission to the alien world is led by Colonel Jonathan "Jack" O'Neil (who was renamed to Jack O'Neill in Stargate SG-1), and Daniel accompanies the military team. Although Jack's mission is actually to assess the threat of alien life and to destroy it if necessary, the team becomes stranded on Abydos. While attempting to figure out a way to return home, they meet and befriend the people of Abydos. They learn that the Abydonians were transported from Earth long ago by Ra, a powerful alien who poses as the Egyptian sun god and who uses the Abydonians as his slaves. Of course, seeing how Ra is evil and bad and tries to destroy Earth, Jack and Daniel help defeat Ra. Daniel, having found a wife and a new home, decides to stay on Abydos, while Jack and the rest of his team return to Earth.
Stargate SG-1 takes place a year after the events in Stargate the movie. The Stargate has been deactivated and kept in storage by the USAF since the mission to Abydos. Jack O'Neill is in retirement when he is called back to active duty. The USAF informs him that a group of aliens- one of whom had glowing eyes like Ra- came through the Stargate and captured an officer before escaping. Jack is sent to Abydos to bring back Daniel, whom the USAF believes may know more about the aliens. Daniel, after his reunion with Jack's team, shows them a pyramid he has discovered, which has an entire database of Stargate symbol sets inscribed on the walls. The obvious inference is that the Stargate can connect to planets, not just Abydos, and so the new aliens must have come from one of these other worlds. Daniel's wife is, in the meantime, captured by the aliens who came to Earth, and so that he may rescue her, Daniel accompanies Jack's team back to Earth.
To summarize the aspects necessary for Atlantis, we learn that Ra (from the movie) and the new alien, Apophis, are two of many parasitic alien creatures that take humans as hosts. These aliens are known as the Goa'uld. Although the Goa'uld use the Stargates for their own purposes, we learn later in Stargate SG-1 that they did not invent them. In fact, the Stargates were built by a race called the Ancients, intelligent beings that were the first evolution of humankind. (The humans of Earth and other planets are the second evolution.) The Ancients apparently disappeared or died out a long time ago, but they left behind their legacy and knowledge in outposts, weapons, and technological items found throughout the galaxy.
At the end of Stargate SG-1 Season 7, an Ancient outpost is discovered under the surface of Antarctica. After Season 8's season premiere, "New Order Part II," a research team, led by Dr. Elizabeth Weir, the former civilian leader of Stargate Command, is sent to the outpost to study the Ancient technology and to hopefully learn more about the Ancients' lost city, Atlantis. This is where Stargate Atlantis picks up.
In Stargate Atlantis, the location of Atlantis is discovered. However, it's in an entirely different galaxy. Dr. Weir and an international team of explorers, scientists, military personnel, and others volunteer to go to Atlantis, with the understanding that they may never be able to return home. The series takes place in this new galaxy with a (mostly) new set of characters and situations, new enemies, and new worlds. Their main objective is to learn as much as possible about the new galaxy and Ancient technology, while at the same time trying to find a way home and fighting off an alien enemy race they have awakened known as the Wraith.
Stargate Atlantis promises new adventures in the distant, and as yet unexplored, Pegasus galaxy when the newly formed Atlantis team is entrusted with the task of investigating the lost city of the Ancients. Sent on a quest to find the ancient metropolis of Atlantis and harvest technology that could benefit all humankind, the newly formed Atlantis team sets out for the distant and unexplored Pegasus galaxy. With only enough power to fuel a one-way trip through the Stargate, the team knows that they may never return to Earth. Upon their arrival, they unwittingly awaken a sinister enemy, the Wraith - a foe so formidable that the encounter not only jeopardizes the lives of the Atlantis team, it seriously compromises their chanse of returning home safely. Worse, they have unleased this plague on a potential new ally, a naturally intuitive race that has to that point managed to survive the ravages of the vampyristic Wraith. Stargate Atlantis was created by Brad Wright and Robert C. Cooper, who also serve as executive prodcuers. They are joined by Stargate SG-1's award-winning writers, with a few new additions to the team.