Initial Goals
Initially the goals of the conflict were to contain the war to keep it from spreading to Asia and Europe and to bar the Soviet Union from joining the North Koreans. I think the goals of the Korean War were unsuccessful because the war became too powerful and North Korea had invaded a lot of Asia.
There were goals to protect South Korea from invasion and takeover by North Korea and to stop the spread of communism in Asia. The goals were met, kind of. Although South Korea remained intact, there was never a formal peace signed, just a cease fire, so technically a state of war still exists between the two countries and tensions have run high between them ever since. While Korea was winding down communist forces in French Indochina were trying to take over the country and oust the French colonial government. We know this country now as Vietnam. So the goal of containing communism wasn't really all that successful.
There were goals to protect South Korea from invasion and takeover by North Korea and to stop the spread of communism in Asia. The goals were met, kind of. Although South Korea remained intact, there was never a formal peace signed, just a cease fire, so technically a state of war still exists between the two countries and tensions have run high between them ever since. While Korea was winding down communist forces in French Indochina were trying to take over the country and oust the French colonial government. We know this country now as Vietnam. So the goal of containing communism wasn't really all that successful.
implications
Other countries had other goals, mostly to benefit their own country in a way. The US/UN had their goals to stop communism and they kind of met their goals.