There is a set of criteria to rate an article B, C, Start or Stub. These are called classes. Similarly, articles can be rated to be of 1 of 4 importance values to a particular WikiProject.
There’s a banner on every article’s talk page. Any editor can change an article’s rating between one of the above classes boldly; if a revert happens, they discuss it according to the criteria.
Some WikiProjects have their own criteria for rating articles. Some of them even have process to make an article A-class.
Before this system, Wikipedia already had processes to make an article a Good Article or Featured article.
With GAs, a nominator should put a candidate onto backlog. Later, a reviewer will scrutinize the article according to criteria. Often, the reviewer asks the nominator to fix quite a bit of issues. If these issues are fixed promptly, or the reviewer thinks that there are only nitpicks, the article passes. If they aren’t fixed in a week or the reviewer thinks that there are major problems, the article fails.
As with other processes, the nominator and reviewer can be anyone, though reviewers are usually experienced.
With FAs, a nominator brings the candidate to a noticeaboard. Editors there then come to a consensus about whether the article should pass.
Both processes display a badge directly on passed articles.
Both processes have an associated re-review process where editors come to a consensus whether the article should fail if it were nominated today
There’s also an informal process called “peer review”, where someone just puts an article at a noticeable and anyone can comment about its quality.
Articles are automatically sorted into categories by their rating and importance. Editors usually look at these to decide which articles to focus on nowadays.