vodka
Vodka is nothing but a distilled spirit. There are many varieties, and price ranges. In recent years flavored vodkas have become the rage.
Vodka can be made with various ingredients such as potatoes, corn, rye, and even grapes. It is distilled at least three times. Many manufacturers claim to distill it at least 5 times.
The more a spirit is distilled, the cleaner the product. This is the reason why the companies advertise their process. It is also a measure of quality. You will find this more expensive products on the "top shelf", literally. These are the ones you want to use in a martini.
Cheaper varieties, in my opinion, should only be used if you are mixing them with fruit juices because the taste will be masked anyhow.
At one point in time Russia and Poland led the market in vodka production. Today, however, many countries including the US produce a marvelous quality spirit.