When I search the internet about which is the strongest currency, the answer is the currency which buys more from other currencies. For example if 1 euro can buy 10 dollars then euro is a stronger currency. But, the conversion rate does not take into account the purchasing power. What if I needed 1 dollar to buy a bottle of water but the price of a european water is 100 euros ? Wouldn’t than mean that dollar is stronger than euro ? Also, I cannot understand why swiss franc is so high since Switzerland is so small country. I mean in order to spend CHF you have to live in Switzerland which most of people don’t so why is it so high valued ?

What if I needed 1 dollar to buy a bottle of water but the price of a european water is 100 euros ? Wouldn’t than mean that dollar is stronger than euro?

No because as you said in the question when people talk about currency being strong they just talk about how much one currency can purchase another currency (see dictionary). These differences in purchasing power are for sure important for making international comparisons. For example, comparing wages in US and UK at an market exchange rate would be less correct than comparing them at Purchasing Power Parity (PPP), which is special exchange rate that factors in the differences in purchasing power. However, when people talk about strength of the currency its just about the market exchange rate.

Also, I cannot understand why swiss franc is so high since Switzerland is so small country. I mean in order to spend CHF you have to live in Switzerland which most of people don’t so why is it so high valued?

Exchange rate has absolutely nothing to do with geographical size of a country. The main factors that determine exchange rate are (see discussion in Copeland Exchange Rates and International Finance):

• relative changes in price level between two countries. If one country has higher inflation than another country you would expect the exchange rate to get weaker.
• interest rate differential between two countries. If one country has higher rate of interest (ceteris paribus) its exchange rate will appreciate.
• Differences in real economic output between countries.
• Balance of trade & Current Account. If country imports more than it exports, or if the financial outflows are higher than financial inflows then that puts pressure on exchange rate to depreciate.
• Speculation & animal spirits. Exchange rate depends also on people's speculation of how it changes in the future as some people trade on forex to make money on speculating how the exchange rate changes. People might not always be rational, animal spirits can make people to be irrationally exuberant or gloomy about particular exchange rate and if too many people trade on those feelings it will move the exchange rate.
• Other factors such as public debt or political stability. If country has unsustainable public debt or political instability that can trigger capital flight from the country putting downward pressure on the economy.

The above are the main factors that come to the mind when talking about exchange rates. Switzerland is country with low inflation, very high real output, it is running trade surplus, has relatively low debt with excellent rating (implying probability of default is near zero), the country is politically stable. Hence, it is not surprising it has strong currency.