Question

what improved relations between the Soviet Union and the United states

Answer 1

Ronald Reagan and Mikhail Gorbachev worked together to improve the relations between the US and USSR.
Gorbachev's policies surrounding Glasnost allowed for a more democratic Russia (and also eventually led to the collapse of the Soviets).

Answer 2

The development of a personal relationship between Ronald Reagan and Mikhail Gorbachev.

US President Ronald Reagan had begun his presidency in 1981 by calling the Soviet Union the "evil empire" and proposing major new defense initiatives to challenge the USSR.  But in Reagan's second term, his rhetoric softened and he developed a personal relationship with Soviet premier over the course of several summit meetings.   In 1987, they worked out together and signed the Intermediate-Range Nuclear Forces Treaty (INF Treaty, a significant step toward arms control and reducing tensions between the two powers.