Zest is the outer part of the peel of citrus fruits. Many graters have a spiky side which is supposed to be for zesting, but it doesn't really work very well. Just use the finest hole-grater you can get your hands on. Even the big-size grater will work.
Lemon, Lime, Orange and Grapefruit can all be zested. If you're planing to use zest for "internal use" and not just as a Garnish (zest is pretty), it's especially important to use organic fruits, as some non-organic citrus are painted with who-knows-what and most will have pesticide residue on the outside. Feel free to zest all of your citrus before using, as zest can be left to dehydrate and then used dry.
Zests have a wonderfully sour-pungent aroma. This is where the essential oils of the fruits come from. Essential oils have many useful medicinal properties. (Fill us in G-Spotters!)
Zests are great for use in teas. Black tea with orange zest is lovely.