The "Sekai o Ōini Moriageru Tame no Suzumiya Haruhi no Dan" (or Haruhi Suzumiya's Brigade to Greatly Enliven the World).
The SOS-dan (or SOS Brigade) was founded by Haruhi Suzumiya in an attempt to create a club that, unlike the rest of the school's, isn't "boring." And more specifically to find espers, time-travelers and aliens not knowing that most of the members are.
High school student Haruhi Suzumiya joined each and every club at North High School for one day before determining that all of them were boring, average, normal clubs. She complained to her friend Kyon that she wanted to be a member of an exciting, different club. He flippantly remarked that she should start one, and it wasn't long before she decided it wasn't such a bad idea.
Haruhi's first move was to acquire a space for the club. She apparently went to the Literature Club's room and found that it had only one member, Yuki Nagato, who acquiesced to Haruhi's request to take over the club room, giving her both a space and eventually another club member. Kyon himself was the official second member, after Haruhi dragged him to the club room. That very day, Haruhi also bullied a second-year student, Mikuru Asahina, into joining.
Kyon eventually was able to sit down and put together paperwork to make the club official (although he doctored the club's "official purpose," which Haruhi stated was to find aliens, time travelers, and espers).
In Japanese, the SOS in SOS-dan stands for Sekai o Ōini Moriageru Tame no Suzumiya Haruhi no Dan (世界を大いに盛り上げるための涼宮ハルヒの団), literally Haruhi Suzumiya's Brigade to Greatly Enliven the World."
In English, to keep the acronym in tact the name was translated to Spreading Excitement All Over the World with the Haruhi Suzumiya Brigade.