Liquid nitrogen (LN2) is really, really cold. Water boils at 212 F, LN2 boils at -320 F.
Its ability to instantly freeze liquids is ideal for ice cream making. Traditional ice cream is made in a batch freezer. Ice cream base (dairy, flavorings, stabilizers) is placed into a cylindrical freezer whose edges are cooled to 22 F. Water in the base freezes and the ice crystals are scraped from the walls by metal blades. When the base becomes the consistency of soft-serve, it is removed and placed in a colder freezer to harden.
Smooth ice cream is achieved by forming the smallest ice crystals possible in the shortest amount of time. LN2 does this by freezing the water molecules on contact. There is also no overrun (air) added to the base, so the resulting ice cream is extremely dense.
To make ice cream this way, simply prepare an ice cream base of any flavor (without mix-ins, they would become rock hard) and place in a large metal bowl. While stirring with a wooden spoon, slowly add liquid nitrogen. Keep adding until desired consistency is reached--it will usually take between three and five liters.
Example: At the Fat Duck, chef Heston Blumenthal serves Bacon and Egg Ice Cream (made using liquid nitrogen) atop caramelized french toast.
**Always be extremely careful while handling liquid nitrogen. However, for a neat party trick, dip your fingers in a bowl of liquid nitrogen for a second or two. The temperature of a human hand is so much higher than that of the LN2, that your fingers will create a pocket of steam in the LN2, and you will not be harmed. This only works for a couple of seconds, so don't get carried away.