Compendium competorum is a fancy term that means a collection of contests or competitions. Just like how you like to have all your toys or games organized in one box, grown-ups like to organize all the contests they have into one book called a compendium competorum.
Imagine you and your friends are having a big competition day with lots of different games like running, jumping and throwing a ball. Each competition has its own rules and prizes. At the end of the day, you have a list of all the competitions, who won and what prize they got. That is like a mini compendium competorum.
Now imagine if you had a whole year's worth of competitions at your school or in your town. That would be a lot of different games, but if you wrote down all the rules, who won and what prizes they got in a big book, that would be a compendium competorum - a book with all the competitions ever done in one place.