First of all, we must realize that the major significance of any war is that which is felt by the people directly affected. The Korean War, in this sense, is significant because it caused the loss of many lives and because it affected so many others in profound ways.
That said, the Korean War was also significant for “bigger” reasons. Unlike in some wars, the outcome itself was not all that significant. Instead, the war was significant for what it told us about geopolitics.
The Korean War ended without any real changes being made to national borders or systems. This was not WWII, which caused territory to change hands and regimes in various countries to fall. Instead, the war ended with the same governments in power in North and South Korea and essentially the same boundaries between the two countries.
What was significant about the war was that it was the first major conflict of the Cold War. It made clear that the Cold War would be a global conflict. It showed that the US was going to perceive any advance on the part of communism as a danger, even if it was half the world away in a poor and obscure country. This set the tone for the rest of the Cold War.