It depends on how you assess the value of the currency. If you simply looked at the current value of the Korean won against the US dollar and saw that it was 1,133 won to a dollar, you would get the wrong impression that the Korean won is weak and that the economy is doing poorly.

Typically, such as disparate exchange rate indicates a poorly performing economy. hyperinflation and currency depreciation are the usual causes of such disparities. However, the relevance of this is only important if the depreciation is currently taking place.

Since it's introduction, the Korean won has gone from 125 to a dollar to 1,133 to a dollar. This is a clear case of currency depreciation, however, except for a spike in 2008, the value of the Korean won relative to the US dollar has hovered around 1,200 won to a dollar for over 10 years.

In the case of Korea, the current exchange rate only indicates that at some point in the history of its currency, there was rapid depreciation. It gives no indication of the current status of the Korean won, which is relatively stable against the US dollar. Therefore, to assess the true strength of the currency, we have to look at its value over time.

Of course, this only works with the Korean won because it's a free-floating currency. These means that the value of the won is set by market forces. Other countries have very stable exchange rates with the US dollar because their currency is pegged to the US dollar. The value of the currency does not reflect domestic economic conditions at all.

In some cases, there isn't an official peg, but countries try to maintain a fixed exchange rate. For example, Ukraine tries to maintain an 8 hryven to a dollar exchange rate, but due to various economic problems, that exchange rate is considered unsustainable by many. Therefore, the stability of the exchange rate does not reflect the reality of the situation.

There is also the unique case of Switzerland wherein the value of the Swiss franc soared a couple years ago due to currency speculation. The Swiss economy wasn't doing particularly better than any other time in its past, but due to uncertain conditions in other European markets, currency speculators started buying Swiss francs. Since Switzerland is a small country, this speculation had a massive effect on the value of the currency. However, since this currency appreciation was not a result of increasing productivity, it was incredibly damaging to Swiss manufacturers and exporters as it made their products more expensive than foreign products.

In short, there are a lot of factors that can effect a currency's value beyond economic health. When looking at the recent performance of a currency, a gradual appreciation generally indicates strength, but look for other factors that might be influencing the currencies value.