In Soviet Russia is a phrase that became famous around the world in the 1980s. It is used to describe a reversal of the usual roles of people in a situation.
Imagine a situation where usually someone in the United States would do something to someone in Russia. With the phrase "In Soviet Russia," it changes the situation: now it's someone in Russia doing something to someone in the United States. It's like the roles have been reversed.
For example, imagine someone in the United States throwing a ball at someone in Russia. Instead, you could say, "In Soviet Russia, the person in Russia throws the ball at the person in the United States!"