The story in the video covers the details and immediate aftermath of the incident quite comprehensively.
This incident have produced a lot of tensions between the US and the SU, at the time when the relationships between the two superpowers had just started to warm up for the 1st time since 1945. The two countries were in the midst of nuclear arm race. Between 1953 and 1958 US UK and SU held 231 atmospheric nuclear tests, some of which were massive. In 1958 an agreement had been reached to temporarily ban testing of nuclear weapons. Negotiations about further restrictions were going along, but very slowly and carefully, as it had potentially very far-reaching strategic consequences for both sides. In 1959 Khrushev came with an unprecedented friendly visit to the USA. But when the U2 incident occurred the trust between the two poles plunged, and the relationships sharply entered another phase of crisis. All negotiations on nuclear test bans were halted, shortly after the moratorium was broken and the biggest explosion ever to ever go off on our planet had been carried out by Soviets.