There are two senses of the word tortilla. The Mexican sense is a flatbread; see entry on tortillas. The Spanish sense of the word is an egg dish very similar to a frittata. In Spain, a tortilla is often called by one or the other of two full names: Tortilla de patatas or Tortilla española.
Like a frittata, a tortilla ends up like an egg pie, or a quiche, except without a crust, and a bit drier. Tortillas usually always involve potatoes, unlike frittatas which can use any ingredient, and while frittatas can be either completely cooked on top the stove or finished in the oven, tortillas are always completely cooked on top the stove. Occasionally a tortilla will use another ingredient. For instance, the tortilla de champiñones uses mushrooms instead, but unless qualified, in Spanish, a tortilla involves potatoes.
Unlike a frittata, where the beaten eggs are poured over the ingredients in the pan, for a tortilla the non-egg ingredients that were fried are removed from the pan, patted dry of oil, then allowed to cool a bit before being mixed into the egg, and then the entire mixture is poured back into the frying pan.
Tortillas can be served hot, room temperature and cold. Aficionados swear that a tortilla is better a day old.
Waxy potatoes work best. The potatoes have to be sliced very thinly. The frying pan should be very hot before you start, and ideally quite deep and non-stick.
Easy way to flip: when it’s all set, use a flipper to ensure that the edges and the bottom are loose. Then put an upside down large plate (as flat as you can get) over top it all, and keep one hand firmly holding that plate in place. Then with the other hand, lift the frying pan by the handle, then flip the frying plan so that the Tortilla will fall onto the plate that you are holding. The cooked side of the Tortilla will be facing up on the plate; the uncooked side will be face down. Put the frying pan back on the stove, then slide the Tortilla just as it is, cooked side up, back into the pan to allow the uncooked side to cook.
A Tortilla will be quite firm and dense when done.
Potatoes are, as emphasized above, the highlighted ingredient. Arguments of course rage as to whether onion should be allowed or not as well. Purists point out that truly authentic recipes don’t use black pepper — and point to this being a sign that Tortillas either originated amongst Spanish settlers in the New World, using the New World ingredient of potatoes but lacking the old world ingredient of black pepper, or that it originated back in Spain amongst peasants, who would have learnt to grow potatoes, but still wouldn’t have been able to afford black pepper. Even though spices such as black pepper were the driving force behind Spain’s explorations, Spain never did find a cheap source of it.