Hockey became popular in the Soviet Union in the years after the Second World War. Prior to that bandy, a sport similar to hockey but played with more players and on a football-sized sheet of ice, was the main winter sport.

In 1946 Anatoli Tarasov, a football player, was asked to form the first hockey team within CDKA Moscow (Central House of the Red Army, later renamed CSKA or Central Sports Club of the Red Army). The reasons for this are not too clear, but sports was seen by the Soviets as a means for them to showcase the superiority of socialism over capitalism, so it may have just been another sport for them to try and dominate in.

Tarasov had limited resources though, seeing how hockey was brand new in the Soviet Union, and with the Cold War it was difficult to gain access to resources and materials from the West. The original sticks used were bandy ones, which I believe are more like field hockey sticks. But in part due to Tarasov's efforts and that Russia, like Canada, is a rather cold country, hockey grew. He soon adopted the methods set out in The Hockey Handbook, written in 1951 by Floyd Percival, a Canadian fitness instructor and athlete. The book was dismissed by most in Canada as amateurish, but Tarasov was devoted to it, and it formed the basis for Soviet hockey, and helped them become a successful team.

In short, it was most likely due to the Soviets wanting to dominate at another sport and putting the resources into hockey to do so, and Russia having a cold climate that traditional hockey countries have, and the popularity of bandy, which is a very similar sport. All these combined to make hockey a popular sport.

Edit: In regards to further reading, there is a few books on Soviet hockey out there:

*The Red Machine: the Soviet Quest to Dominate Canada's Game by Lawrence Martin is supposed to be the definitive account, but I've never been able to find a copy, and that's not likely to change soon as used copies are selling for $160 on Amazon.

*Red Line: Soviets in the NHL by Stan Fischler includes some history, but again that is a scare book to find (I found my copy by total chance).

*Breakaway: From Behind the Iron Curtain to the NHL--The Untold Story of Hockey's Great Escapes by Tal Pinchevsky is more about defections in the 1980s, but I believe it also covers some earlier details.

*ESPN also wrote a decent introductory piece back in 2002: Russians regroup on other side of the red line by Jeff Marron. It should help give a little more detail for anyone interested.