Troika is a Russian work which orignally referred to a special way of driving three horses in a carriage or, more usually, a sleigh. In a troika the horses are three abreast (ie, they all pull together in the same line, rather than having a lead horse at the front as is more typical for horse-drawn team carriages using three or more animals). In a traditional troika the horses on the outside lead, and usually canter while the middle horse trots. However, the word is often used to refer to any horse drawn vehicle where the horses are three abreast.
Troika derives from the Russian word for three and the carriage goes back to the 17th century; they were originally developed as a faster means of delivering the mail.
The word was then used to describe a dance where one man dances with two women, and nowadays it is often used in a political sense, to describe a group of three judges or another group of three people who are in a judicial position - for example, the three institutions who organised the recent financial bailouts in Europe.