Many countries seem to have been born rich. This means that the country gained its independence or was settled there and their economy was strong from the very beginning. Often, the way this happens is because the country has some kind of valuable item that is either mined, grown or a service that they provide.
Luxembourg seems to be rich because they have thought of ways in which their economy is structured. It provides a lot of banking and financial services. Any time a country can create banks and loan money, it will most likely be a rich country. A lot of people try to evade paying taxes in their own country. The way they do this is by putting their money in another bank account in another country.