Little is known about Mamma Gkika's just yet, but based on Gil's statements, it used to be a bar that served Jägers before the fall of Castle Heterodyne. From what can be determained so far, the bar is currently a tourist trap with barmaids dressed as Jägers and run by Mamma Gkika herself. It also features a rather salacious, but glowingly-reviewed burlesque act, also done by the barmaids dressed as Jägers. From the tenor of certain comments made by the staff and judging from the decor of the interior rooms, it may be that it is also a Jägerbrothel.
However, Mamma Gkika's is also the location of an underground medical facility. Since the Jägers won't let anyone but a Heterodyne operate on them (since a Jäger is considered to be proprietary information, even by the Jägers), Jägers who get too banged up to fight come to Mamma Gkika's to recuperate. (AN: given the extraordinary resilience and healing properties of a Jäger, it's rather terrifying to think of what has to happen to make a Jäger unable to fight). Mamma Gkika "patches them up," using some rather sparky medical devices and a hefty dose of Battle-Draught, so that they are stable enough to be properly repaired by the Heterodynes, when they return. Given how many Jägers seem to be in the bar at the current time, Agatha Heterodyne may have an extensive line of patients to deal with when she emerges from Castle Heterodyne.
After his defeat of the Knights of Jove, Gil was escorted there by Da Boyz to conceal the injuries he sustained in the process. There, he was subjected to, and survived, Jäger field medicine. Which, according to the proprietress, might mean that Gil is somewhat more than human...
Just how secret Mamma Gkika's is, is unknown. The Boys know of it, and somehow Zeetha was able to find him there. In addition, Vanamonde von Mekkhan and Krosp were able to find their way as well. Given the tourist trap nature of the place, and the "hiding in plain sight" philosophy of the owner, it may be that everybody knows that there is a Mamma Gkika's, but few know exactly what it is.