GTA Online normally starts a new event week on Thursday. That is when Rockstar refreshes weekly bonuses, discounts, challenges, rewards, and rotating selections. The current event period and its end date are shown at the top of this page because Rockstar sometimes extends an event or uses a different schedule.
A weekly reset is different from a daily reset or a mission cooldown. Daily objectives and daily limits refresh on their own schedules, while replay timers usually begin when you finish an activity. If a guide says a reward is available on your first completion after the weekly reset, it becomes available again when the next GTA Online event week begins.