In addition, Gorbachev was willing to negotiate new arms limitations treaties with President Reagan, labeled START (Strategic Arms Limitations Treaty) which, for the first time in the Cold War, reduced the amount of nuclear weapons in each country's arsenals.
In turn, Reagan was willing to take medium range Pershing nuclear missiles out of Europe, making the USSR feel more secure, and laying the groundwork for future progress as well. Lastly, the Soviets pulled out of Afghanistan in 1988, ending an eight year war. We had supplied the Afghans with weapons to fight the Soviets, so the end of the conflict removed a source of tension too.
The main thing that led to the easing of these tensions was Mikhail Gorbachev. Gorbachev instituted policies and showed an attitude that helped to ease tensions with the US.
Gorbachev's policies of perestroika and glasnost showed that he was willing to (and that he wanted to) move the USSR toward a more open society. This implied that he would be less hostile to the United States.
Gorbachev also helped ease tensions by being willing to do things like meet with Pres. Reagan at a summit meeting in Iceland. His personal rapport with Reagan helped as well.
The outcomes of this change include the collapse of the Soviet Union and the end of the Cold War.