Mongolian barbeque is a style of cooking. It manifests itself in a few different restaurant chains, like the "Mongolian Grill" in canada (maybe elsewhere too, but I've mainly experienced them in southern ontario).
Mongolian grilling is essentially barbeque in that it's cooking over an open flame, but using *Huge* flat cast-iron grills, supposedly based upon the historic mongolian tradition of cooking on their shields over an open fire.
The food itself is essentially do-it-yourself stirfry. Strips of meat (many different kinds to choose from) which historically would have been carved off of the catch-of-the-day with the warriors' swords, a good selection of vegetables to round it out, various flavored oils to prevent sticking, and many many types of sauce to add, from sweet to fiery, topped off with your choice of herbs and seasonings.
The dining experience goes roughly like this:
You pick up an empty bowl from the stack and head to the food line. You select your meat(s) (steak, chicken, turkey, pork, lamb, sausage, fish, calamari, shrimp, etc) - as much as yo like. You pick your favorite veggies, again, as much as you like. You pour on at least one ladle of oil (sesame, olive, garlic, etc), and two ladles of sauce (everything imaginable from sweet&sour to mongolian fire sauce - HOT HOT HOT, to caribbean jerk, to italian herb wine & tomato sauces), and then season it how you like. You take your bowl to the grill, where the chefs take it from you and plop it down on the vast iron grill, smacking it around with long sticks to break up the meat and ensure everything is cooked right. Once that's done, they give it back to you in a new bowl, and you go back to your table where you find flour tortillas and steamed rice. You can then eat your meal as a stirfry with rice, or roll it up in a toritilla. Either way it's tasty.
If you have such a place near you, I encourage you to try it. If the food's no good, you have only yourself to blame! *lol* Actually, I know some people who find this intimidating, as they can't think on the spot as to what might go good together. While I don't empathise at all (how can you not know what you like?), they do try to help you out by posting many "recipes" that the not-so-creative can try with a reasonable chance of success.