Sorry... DX is short for a distance contact, so someone outside of your country. There are 340-odd "DX entities" defined, some of them incredibly rare (Bouvet Island, North Korea), and people spend their lives trying to get the ones they're missing. Other people will gather a group and raise funds to go to those places so that they get on the air.

Contesting is when there's an event, usually over a weekend with a set of rules and a point system for contacts. People get on the air and try and get the most points by making contacts. Big contests might have 10 or 20 thousand people all over the world participating and top competitors are running 2 or 3 radios simultaneously to get rates of over 400 contacts an hour. But there's also smaller contests such as QSO parties where a State tries to get people from every county on the air and people from across the country try to work them. Or silly ones like the Zombie Shuffle at the end of this month where people make up funny names and exchange them at low power, low speed Morse code just for fun. https://www.contestcalendar.com/ shows all the contests and gives you some idea of the variety.

Since some of the less popular countries tend to get active during the big contests, many DX'ers will enter contests just to find a few more.