Originaly they started out with a Movie called Stargate 1994
And from that point forth, they launched a serie called Stargate SG-1.
It's a sci-fi serie, and the story goes as followed:
They find a large 'Ring' in Egypt, which had the ability to travel to other 'Rings' across the universe.
These 'Rings' were called Stargates, thus the title 'Stargate' in the movie and the serie names.
Within these series they seek out new civilisations of which they can gather friendship and diplomatic relations with..
..Or, at least they hope/intend to..
These Series (there are multible series launched, namely, Stargate Atlantis, and Stargate Infinity) are filled with humor, action, companionship and so on.
But I believe you can get a better view on these series if you've watched a few episodes.
Though it is recommendable to start with Stargate the Movie, there is a rather large gap between the Movie and Stargate Atlantis, and thus it is also recommendable that you follow with SG-1, but that of'course is just a recommendation.
Regards,
R.