See the notes for information on some of the ingredients. You'll be whipping the whites, so put them in a large enough bowl. The acidity of the juice thickens the milk and eggs into a custard. If you like, run the pie under a hot broiler for a minute until the egg whites are slightly browned. It shows up on postcards, place mats, lime juice bottles, and guide books.
Some people fold a little of the beaten egg white into the custard to make it lighter.
Some put sweetened whipped cream on top rather than egg white. Some use two or four eggs. Traditionally, this pie is made from the juice of the Key lime, a small yellow citrus fruit quite different from the larger and more familiar Persian lime. Key limes are very sensitive to cold and in the U.S. have never been grown above the very southern tip of Florida. Bad weather and disease have killed off so many of them that the only remaining grove is a private one on one of the Keys, so you cannot buy Key lime juice in the U.S. any more.