The Gauntlet is a piece of technology, used by The Hosts.
It was first seen at the end of Season 1, and appeared to be part of the suit worn by the VIP that Broussard, Katie, Morgan, Simon and BB accidentally killed when the bomb in the train tunnel caused a bigger than expected explosion. The members of the cell removed the device from the suit and took it with them when Katie warned them that Homeland was on its way. They were forced to leave the VIP's body behind.
The gauntlet was seen again in Fallout, where it was being examined by BB, who was very sick. Later in the episode, it was discovered that BB was suffering from a fatal level of radiation poisoning. After this, Broussard removed the device and placed it in the custody of Hennessey, for safekeeping. In Tamam Shud, Hennessey is found killed and the Gauntlet is missing from his headquarters when Katie and Broussard search it after finding Hennessey dead in a movie theater.
At various times at the beginning of Season 2, it is mentioned that the Resistance has an "artifact" that belongs to The Hosts, and it is presumed that this Gauntlet is that artifact.
At the end of Tamam Shud, Will and Broussard meet Noa, a resistance member from outside the wall, who says, "The real war is about to begin, and that thing you stole is going to help us win it." It is presumed that "the thing" they stole is, again, the Gauntlet.