Exo-Frames are robotic suits or armor that give a wearer added strength, protection and/or offensive ability. Some also enable flight.
David Xanatos owns and operates several exo-frames.
The first was modelled after his Steel Clan robots, themselves built to resemble Goliath. Unlike the Steel Clan, the Gargoyle Battle Armor is colored red and has four fingers as opposed to three. Beyond that it outwardly looks identical to a Steel Clan robot. The Manhattan Clan initially believed that it was a prototype advanced version of a Steel Clan robot.
Originally built by the Scarab Corporation, Xanatos debuted his battle armor when he stole the Eye of Odin from the Museum of Modern Art as part of a scheme to locate the Manhattan Clan's new home. Xanatos led the Steel Clan and fought the Manhattan Clan at the Statue of Liberty. Although he was thwarted, he did manage to fight Goliath to a stand still. ("The Edge")
Since then, Xanatos has made use of the armor on various occasions such as helping to break Demona's stone-by-night spell and trying to capture Coyote the Trickster. ("City of Stone", "Cloud Fathers")
Xanatos' armor is equipped with rockets on the back and feet which allow him to fly at extremely high speeds, and he maneuvers with razor-sharp wings. There is a particle beam cannon located on the right arm and on one occasion he fired a device from his right shoulder designed to overload and destroy a Steel Clan robot.
Xanatos is able to operate the suit through a combination of an options scroll on his internal visor and internal sensors. He trained a long time to use the suit proficiently, and it's tailored to him specifically. 
Xanatos has the ability to disassemble his battle armor into a more compact suit of armor that he can conceal beneath an overcoat.  This suit still allows him enhanced strength, limited flight via a jet-pack on his back and armored talons on his hands. ("Eye of the Beholder", "Double Jeopardy")
After the Pack barely escaped the Manhattan Clan, they were approached by Coyote 2.0 on Xanatos' behalf and offered upgrades. Not wanting to lose his humanity, Dingo chose a robotic suit of armor, constructed by the Scarab Corporation. ("Upgrade")
Dingo's armor was capable of flight and featured concussion blasts from the hands; a particle beam that rose from the right forearm; and a built-in modem. It also increased his strength and durability. The armor could also be operated by Dingo via a remote control.
Eventually, Matrix merged with Dingo's armor, consuming it, and has since become Dingo's new exo-frame, bonding with Dingo's central nervous system when the two are merged. When acting as Dingo's exo-frame, Matrix still enables flight as well as new abilities (such as growing another set of arms out of the armor's back). Presumably, Matrix can duplicate all the previous exo-frame's abilities as well. ("Walkabout", "Strangers")
While conducting thefts of high technology in order to lure out the Manhattan Clan, Demona stole an exo-frame from the Goldencup Bakery Building. Goliath, Angela, and Brooklyn were able to bring her down, destroying the suit in the process. ("The Reckoning")
The armor possessed rockets on its back allowing it to fly, a cannon capable of firing a particle beam on its left arm, and a claw on its right. Another defense mechanism included the suit being able to generate electricity along its skin, giving anyone who came in physical contact with it a nasty shock.
Their armor allowed them both enhanced strength and durability, as well as flight. Jon was protected in his armor from a direct attack from Hudson's Sword.
Jon's armor featured a large particle beam cannon on the right hand and a claw-like left hand. Robyn's did not sport these features. ("Hunter's Moon Part Three")