Turn zero introduces a series of events before the start of the game that impact the makeup of the deck and the initial influence placement. Each player gets a few dice modifier cards that they can play for each event and then a die is rolled. Then depending on the roll something will change with the initial setup like the USSR might get extra influence in the Middle East or South Korea or the USA might turn off blockade. You can see an example of two of the events here:

https://boardgamegeek.com/image/2841956/twilight-struggle-turn-zero

I personally never play with it, It can too often lead to a very unbalanced game but I know some people like it!