Years of tension between the USSR and PRC came to a head in 1969. Then a simmering border dispute over islands in the Ussuri River turned to actual conflict. PRC forces attacked and killed Soviet border guards on Zhenbao Island, and the USSR retaliated by shelling PRC positions and moving tanks against them. [Source]

Because of this the Nixon administration became concerned that the USSR might invade the PRC and that it might be an opportune time to renew diplomatic relationships with the PRC. Mao Zedung was similarly inclined. After a chance interaction between US and PRC ping pong teams in Japan, Mao invited the US team to visit China. [Source]

Shortly thereafter Henry Kissinger, Nixon's Secretary of State, arranged to travel secretly to Beijing and begin negotiations between the two countries.

At that time, both PRC and ROC wanted "one China". The only question was whether the capital was Beijing or Taipei. Mao and Zhou Enlai signaled to Kissinger that while they remained committed to a "one China" policy, there was no timetable for reunification of Taiwan.

Kissinger wanted assurances that PRC would not support North Vietnam militarily and, again, got assurance from Zhou Enlai that while China had a special relationship with the Vietnamese it would not get involved.

To have PRC as a potential ally against the Soviet Union and to have it not meddle in Vietnam were worth the price of throwing Taiwan somewhat under the bus.

Kissinger discusses the above in detail in his book On China