What I've learnt from South Korean history (roughly, from one of my liberal arts classes) is that because of their geographical disadvantage, they were invaded by China and Japan numerous times in the past. Moreover in the modern history, the Japan empire colonized Korea during WW2 and the peninsula was more or less a fireground of the US and China right after WW2. Without a doubt South Korea was one of the poorest nation in the 60s and 70s, but since 80s, the country have developed rapidly and just like some indexes (GDP and HDI, etc) indicate, the nation has become one of the most developed nations in the contemporary society. It made me really curious while all other developed nations, except S. Korea, had abilities like infrastructures, colonies, resources, technologies etc. My question is what happened in the 80s or 90s in S. Korea? How the nation became so successful?
This Wikipedia article is so quite enough. You should have researched more.
By creating favorable policy directive for economic development as preceded by Japanese economic recovery as the logistic supplying bastion for American troops in the Korean peninsula during and after the Korean War, South Korea's rigorous education system and the establishment of a highly motivated and educated populace is largely responsible for spurring the country's high technology boom and rapid economic development. Having almost no natural resources and always suffering from overpopulation in its small territory, which deterred continued population growth and the formation of a large internal consumer market, South Korea adapted an export-oriented economic strategy to fuel its economy, and in 2014, South Korea was the fifth largest exporter and seventh largest importer in the world. Bank of Korea and Korea Development Institute periodically release major economic indicators and economic trends of the economy of South Korea.
It is always difficult to answer the question "why"? It is a combination of many reasons. Perhaps some reasons can be unveiled by comparison. It seems that "good government" is very important for prosperity of a nation. Compare S Korea with N Korea: same people by the way. I do not know the whole history of Korea very well, but I suppose there was no substantial cultural differences between the North and South before 1940s. Differences which could explain the current disparity in the economic development.
Then one can ask where does "good government" come from. Someone said that "people have the government that they deserve", and this explanation is popular. But comparison with N. Korea again leaves a puzzle: why S. Koreans and N. Koreans "deserve" something different?
So where their government comes from? In 1940s the United Nation vigorously resisted the "unification" of Korea, and gave a mandate to US troops to defend it. The US troops were successful in maintaining and supporting the S. Korea government system. In 1970s, it was different with the similar case of Vietnam. The attitude of UN and US was different. Unification happened. And the results we see now.
It is interesting to notice that some most developed countries, Germany, Japan and S. Korea, all have a common feature in their history: victorious US troops on their territory in 1940s or 1950s. Soon after that a vigorous economic development followed.
I do not want to claim that this pattern continues. It does not. And in general, I do not pretend to have a complete explanation. The question is indeed difficult, and I just brought attention to some patterns.
Speaking of the ancient history and many invasions. Well, how many invasions did England and France experience in the old times? Germany even did not exist as a state until the end of 19s century. So this does not seem to be very relevant for the present situation: one probably has to look at more recent history.
Remark. Of course I understand that Japan and Germany were the most powerful nations in Europe and Asia, respectively, before 1940s. But comparisons with other nations in the Far East, like N. Korea and Vietnam, seems legitimate. One can also compare with former British colonies, Hong Kong and Singapore, which are also doing better than the countries surrounding them. I suppose there was a strong British hand in establishing good government there.
If someone's willing to know how South Korea was developed, then the person must look for the remarkable achievements by President Park Chung-Hee (14 November 1917 – 26 October 1979), the 3rd President of South Korea . Though it'll be a book length answer to give a full answer to the question. I'll try to write down some about Korean history in the President Park's years.
Background. In 1969, US President Richard Nixon announced a new direction in American policy toward Asia, called the Nixon Doctrine. The policy in a nutshell was to downscale the US forces in Asia and to let Asia handle their problems on their own. At that time President Park foreboded there will be blood wind in Asia by communists , so he tightened up the national security by reforming the constitutional law, called Yushin constitution , and it was effective in tightening up the national security. So South Korea was kind of safe from the communization.
60s. In 1963, President Park was very impressed by the strong infrastructures of West Germany when he was invited in West Germany (he was especially impressed by the Autobahn, right after his return he planned the construction of the first Korean expressway, Gyeongbu expressway). He consulted with Ludwig Erhard (Chancellor of Germany at that time) about the successful economies of West Germany, namely Miracle on the Rhine River. Since then West Germany helped a lot in reconstructing South Korea, recruitment agreement and conclusion of Technical Cooperation for instance. Analogously to Miracle on the Rhine River, the successful economies of South Korea is usually called the Miracle on the Han River.
70s. Just like you mentioned in the question, Korea had no infrastructures, nor natural resources, nor technology and no colonies in the past. Korea had nothing to sell in the world market, also had no abilities. Back then South Korea exported wigs, at best. In the 70s, President Park planned to promote heavy and chemical industry. Every economist thought these radical policies will naturally fail, but due to the hard work of Koreans, the industry flourished. It will be a book length to provide proper details on this.
 : At first, President Park seized power in a military coup for his first period of president. Because at that time South Korea was poorest country with incompetent heads, there was the Military Supreme Council for National Reconstruction formed to rebuild the whole nation. He was the second chairman of this council and he seized power during his chairman. Afterwards the electoral system was reinstated, then he was elected 4 more times with overwhelming supports from Korean people due to his miraculous achievements.
 : In fact many Asian countries become chaotic after the Nixon Doctrine. Communization of Vietnam, cultural revolution in China, Cambodian genocide, civil war in Philippines and Bangladesh, et cetera. Even in middle east there were invasion of USSR in Afghanistan and 1973 Arab–Israeli war. There were many threats by North Korea in South Korea. Lots of spies were infiltrated in South Korean society, and lots of armed communist guerilla broke in to South Korean territory, some of them even made it to Seoul.
 : There were some clauses in Yushin which was aimed for prolonged ruling of President Park and some other clauses are considered as anti-civilrights in now days, but since South Korea was (and is) democratic country, Yushin was held through elections better or not. Though because of the clauses President Park is considered as dictator now days.
Their children study 16 hour days and their workers average 2,163 hours per year. With regards to the steep increase they are very capitalist which is China's downfall. http://www.bbc.co.uk/news/education-25187993 https://en.wikipedia.org/wiki/Working_time#South_Korea