The ESO Weekly Trial is a weekly trial leaderboard in The Elder Scrolls Online. Each week a different trial is selected and players can complete the trial to try and earn a place on the weekly leaderboard. Players who get onto the leaderboard for that week will earn an additional reward mail with Legendary quality gear.
Each server, for example PC NA and PC EU, has a different Weekly Trial and Weekly Solo Challenge. This page will tell you which one is currently active on your server.