What were the reasons for this? How was the United States affected by their decision?
The very short answer to your question is: Woodrow Wilson.
Although entire books have been written on your question, a succinct answer goes something like this:
Woodrow Wilson treated both the negotiation and ratification of the ToV as his own personal quest. He ignored the significant political divides in America, and believed he was charming, intelligent, and on-a-mission-from-God enough to achieve all he thought best. The group he brought with him for the negotiations included one minor, unimportant Republican, and when he brought the highly contentious treaty home, he refused to accept any reservations (meaning basically attached loopholes).
Henry Cabot Lodge and Wilson hated each other, but, possibly due to strokes or possibly because he was stubborn and short-sighted, Wilson refused to in any way compromise with Lodge, making it rather easy for Lodge to stir up both isolationist support and the so-called "Irreconcilables."
I'm sure some will disagree, but the biggest reason comes down to the way Wilson handled the treaty process. As for how the U.S. was impacted, widen your gaze. Zara Steiner has fairly convincingly argued that if the U.S. had been an active member of the League of Nations, and the international community after the First World War, there likely would not have been a second.
One of the biggest reasons was Woodrow Wilson's 14 points which he wanted the Treaty of Versailles to follow along. As well as a contributing factor being the United States isolationism; they were trying to stay away from European Politics. The US congress disapproved of many of the Fourteen Points, especially the League of Nations which was Wilson's great ideal and the thing which he fought he hardest for during the meetings of the Treaty of Versailles. The US government did not want to be part of the Treaty of Versailles, and many historians argue that since the Loge of Nations was lacking in a nation strong enough to be the leader, which the US could abbe been that the League would not have collapsed and maybe the Second World War would not have broken out.
So while Woodrow Wilson was one of the contributing factors to the Treaty of Versailles not being ratified by the United States, the growing ideal of isolationism made the American government wary of any outside agreements, including the Treaty of Versailles.