Categories are an important wiki idea. They help with organising pages and make it easy to discover pages that are related.
Using Categories is easy: You just have to write the name of the category on the page and you are done. It will become a member of that Category. MoinMoin even simplifies this by letting you choose from a list of available categories while you are editing the page. By the way, this page is in the category CategoryCategory.
Every category has a page on which all its members are listed. The page of a category is also used to describe its contents. If you want to get a list of all pages in that particular category, either click the title of the category or insert a suitable macro which lists the pages:
[[FullSearch(CategorySamples)]] lists all pages in the category CategorySamples
[[FullSearch(r:CategoryRecipes\b -r:CategoryCake\b)]] lists every recipe if it is not about a cake
See HelpOnSearching for further information about the syntax.
Normally, categories have to named like CategorySomething. If you want to allow other patterns like CatégorieGaffeur (that is french by the way), then the administrator needs to change the configuration option page_category_regex according to the users' language. In a hebrew wiki, you would use page_category_regex = '^Category[A-Z]|^קטגוריה .+'. See HelpOnConfiguration.