Their name is a reference to the Sixth Pilgrimage, of which all current Sixers are from. However, not all humans who came through the portal on the Sixth Pilgrimage are Sixers. Some of them stayed at the colony when the Sixers first went OTG (Outside the Gates).
The Sixers were sent to Terra Nova to try to overthrow Commander Taylor. They, along with Lucas Taylor, are trying to create a portal to be able to go back to the future so that they can use Terra Nova's resources. If Mira succeeds, she can see her daughter, Sienna, who is still in 2149.