That is, if you want to have the high currency, you have to exchange more of your local currency for the higher currency and that strengthens higher currency more while the lower or cheaper currency keep depreciating. Also it will help foster more international benefit and advantage in trade. It will be cheaper for investors from strong currency to import goods and they have more products than what investors from lower rate currency would get when they are importing or exporting from higher currency country.
Yes those are all benefits of a strong currency but there is also a downside here which is when the currency is strong, the exporters in that country will be less competitive since less foreigners will be interested in buying in their currency. What can be done to offset this disadvantage is if the strong currency sold to stronger currencies.
Yes a strong currency reflects the status of an economy. A strong currency means a country has low inflation, low national debt and a high GDP growth. This also might mean that the country's trade is doing well signalling a strong economy.