The series and movies are centered around an alien technology called a stargate. It creates a connection with another stargate by creating a wormhole between them. Stepping into the stargate transports you to the other stargate almost instantaneously.
After the discovery of the stargate, the series focus on the exploration of the universe by the human race, making friends and enemies along the way.
The Stargate franchise began with the movie "Stargate". The "Stargate: SG1" series starts several years after the events of the first movie and ran for 10 seasons. The movies "Stargate: Continuom" and "Stargate: The Arc of Truth" wrap up the main story lines of the series. The "Stargate: Atlantis" and "Stargate: Universe" series are both spin-offs of the main series and ran for 5 and 2 seasons respectively.