The Alliance of European Republican Movements is a group of people who believe that countries should not have kings or queens, but should instead be run by elected leaders. It's like when you and your friends vote on what game to play, instead of just one person saying what to do.
But the Alliance doesn't just want each country to be a republic, they want all of Europe to be republics. Imagine if your entire neighborhood decided to play a game together instead of each person doing their own thing - that's what the Alliance is trying to do with European countries.
This group also wants to promote equality and fairness, so that everyone has the same chances and nobody is treated differently just because of who their family is. This is like if your parents gave you both the same number of cookies so that you didn't feel left out.
Overall, the Alliance of European Republican Movements wants people to have more say in how their countries are run, and for everyone to be treated equally.