Horseradish is a member of the cabbage family of plants which also includes watercress, mustard greens, broccoli and radish. While the leaves of the horseradish plant are edible, the roots are more commonly used.
What we are interested in here is called horseradish or "prepared horseradish" in the store which is chopped and preserved with vinegar in a jar. You will find this usually in the cooler at the grocery store often by the cold pickles, sandwich meat, and sausage. Do not buy "horseradish sauce" which is mixed with mayonnaise, usually found in the condiment aisle at room temperature and not suitable for drink recipes.
The real thing is what you're after. Prepared horseradish is quite hot with a briny, bracing flavor. You don't need to use much (unless you are a heat freak like me) and that little jar will keep for many months in your refrigerator.
The most common use for horseradish in the cocktail world is in Bloody Marys. A Bloody Mary recipe with horseradish in it usually deserves examination. Other sources of heat such as Tabasco, cayenne and fresh chili peppers are great, but horseradish has a unique style of heat that goes well with the other savory ingredients in a Bloody Mary.
One other place I have see this root used is horseradish vodka. You can find it at the liquor store or make it yourself. If you make it don't use the prepared product in the jar - instead you need fresh horseradish root. I have tried some of this house made at a bar and it makes a great Bloody Mary.
Do you use horseradish in other drinks?