The Kitchen Debate, as the episode is colloquially called, was important as it laid a groundwork for US-Soviet detente, that unfortunately failed to materialize.
The debate was interesting as the talking points of both sides had less to do with an Geopolitical posturing and more to do with how both governments treated their citizens and the advancements made in quality of life for their respective nations. Khrushchev famously telling Nixon that the Soviets would soon overtake the US and wave 'bye bye' as they zoomed past. However, beyond just the scope of the debate it allowed Khrushchev to propose to the US visitors his desire to visit the US, something no other Soviet leader had done before. If Nixon had overplayed his hand and was far more hostile, the Khrushchev visit may have never materialized.
To illustrate the point that was being made here, in this example of an average American home in the middle of Moscow, was the words spoken to Nixon by Khrushchev saying "On politics, we will never agree with you. For instance, Mikoyan likes very peppery soup. I do not. But this does not mean that we do not get along."
This phrase illustrates the debate in the Kitchen, but also Khrushchev's ideas of US-Soviet relations. That even though we do not agree on politics, we can still get along, that we do not need to be enemies simply because our politics are vastly different. Nixon was on the same page, expressing such on a handwritten note prepared for the meeting:
In other words, peaceful competition.
These ideas of peaceful co-existence and the friendly debate with Khrushchev may have paved the way for the actual detente under the Nixon presidency years later.
The problem with the debate and why it is often sidelined is because it was the start of something that never materialized. For the debate led to the visit of Khrushchev to the United States which opened the way to further thawing of US-Soviet relations. Khrushchev met with President Eisenhower at Camp David and concluding the meeting with Khrushchev inviting Eisenhower to visit the Soviet Union soon. However, what ended up happening was that the Eisenhower administration continued Military Surveillance of the Soviet Union using spy planes. Unfortunately, one was shot down over the Soviet Union leading to the capture of a US airmen Francis Gary Powers. During the announcement that the Soviet Union had shot down a US plane over the Soviet Union, Khrushchev did not mention that the crewman was alive, leading to the US to deny that it was military operation and instead saying it was a NASA airplane and it was civilian in nature. This led to Khrushchev springing the trap on the US by saying:
I must tell you a secret. When I made my first report I deliberately did not say that the pilot was alive and well ... and now just look how many silly things the Americans have said.
The U2 spy plane incident led to an icy summit in Paris, where the focal point was on the fact that the US was spying and then the attempted cover-up. Ultimately it contributed to the failure of a US-Soviet *detente* and instead led to the placing of Nuclear Warheads in Cuba, leading to the Cuban Crisis. If the U2 incident never happened, it would have seemed likely that a detente could have occurred, which would have made the Kitchen Debate in essence the start of Peaceful Co-existence. However, events occurred that prevented that to happen.