"Weekly reset" refers to a scheduled time when certain activities, progress, or rewards in a game or system are reset or refreshed every week. Full definition
Bungie has just shared details on Destiny Weekly Reset for October 20 week. (gamepur.com)
We also have guides for weekly reset activities, such as the return of Iron Banner, the Pyramidion Nightfall and solutions for all Treasure Map locations, as well as regular planetary activities like Flashpoints, Heroic Public Events and Lost Sectors. (eurogamer.net)
If nothing takes your fancy, then wait until the next weekly reset for a new inventory to appear. (eurogamer.net)