In common parlance, members of any family which reigns by hereditary right are often referred to as royalty. Some countries have abolished royalty altogether, as in post-revolutionary France and Russia. But in many countries they still command significant power.
In certain monarchies, such as that found in Saudi Arabia or Kuwait, the monarch actually exercises executive power. In most constitutional monarchies, however, members of a royal family perform certain public, social, or ceremonial functions, but refrain from any involvement in electoral politics or the actual governance of the country.
Look at the world's richest surviving royal families, who continue to enjoy vast resources.