This is the granddaddy of molecular gastronomy. Originally used by Ferran Adria at el Bulli, the technique of 'spherification' has been imitated around the world by chefs looking for a simple way to impress diners.
A hydrocolloid is a substance that forms a gel on contact with water. They are usually polysaccharides (sugars) or proteins that are capable of thickening and gelling a liquid.
Hydrocolloids are usually derived from natural sources; agar agar and carrageenan are extracted from seaweed, gelatin from mammal bones, and pectin from citrus peel. They have been used for decades to thicken jams and jellies, and gelatin was made popular by its use in Jell-O.
Chefs have begun using hydrocolloids like xanthan gum and sodium alginate to "spherify" foods.
The simplest method is to enrich some liquid (usually a fruit or vegetable puree) with calcium chloride. The thickened liquid is the spooned into a bath of water and sodium alginate and left to sit for a minute or two. The two chemicals react and a thin gelatin-like layer surrounds the liquid. The spheres are removed from the bath and rinsed with water. Upon consumption, the sphere "pops" in the mouth, releasing the liquid interior.
Usually used for their "wow" factor, spheres are a great way of delivering an intense shot of flavor in a small package.
Some restaurants are beginning to experiment with using an ice cold bath of grape-seed oil instead of sodium alginate. I have used this technique with pea puree and mango juice and found it to work just as well--if not better--than the alginate method.
The original. el Bulli olives, spherified olive juice.
Carrot "caviar", made using a syringe adding the puree to the alginate bath drop-wise.
A dish I had at Alinea based around butter. Combined all the elements we usually associate with melted butter (crab, popcorn, sweet corn). The yellow orb near the center of the dish is a sphere of melted butter. The sphere is meant to be nudged open--the butter acts as a sauce for the dishes components. Not low-cal, but so delicious.
This last picture is just to show that the chloride/alginate technique doesn't have to be used for spheres. While staging at Jean-George I made components of the dish below, a scoop of vanilla ice cream sitting atop chocolate noodles in a peppermint broth. The noodles are made using hydrocolloids and are extruded into an alginate bath using a thick-tipped syringe. On my last night there I tasted the dish, and when you get a bit of every component at once, it tastes exactly like mint chocolate chip ice cream.