iRacing has four Seasons each year. Each season consists out of 12 weeks with serious racing. When we say serious, we mean the type of racing that matter when it comes to your iRating and division. Week 13 isn't listed on these schedules, but rest assured you can count on it four times a year!
During week 13 there are less events scheduled, yet those that are scheduled are more focused on having fun. Think of crazy track & car combinations and opening up a ton of content for everyone to enjoy. During the Week 13 events, the player does not earn (or lose) and Safety Rating or iRating. This makes the week overall less serious as there essentially is nothing to gain or lose, besides having a blast on the track.
So now you know that whenever people refer to Week 13 they mean the end of the season which could also be seen as an off week for those that are running full seasons as they can decide not to compete without suffering any penalty or not earning points.