The Soviet Union turned back their ships on their way to Cuba due to a naval blockade set up by the United States.
This blockade by the United States was done after they found out that the Soviet Union had missiles in Cuba that could hit almost every American city. The US government was worried that the Soviet Union would continue to bring in weapons as a means to prepare for war. To stop this from happening, the US Navy set up a blockade which would prevent the Soviet Union from getting any more weapons into Cuba.