After Darkshore became a Warfront, the old zone also got updated to have level 120 content. It also got a brief update for the end of the Legion expansion pack, but it has now been updated again to fit level 120 content.
The zone has 5 World Quests available each 24 hour cycle. Only one faction will be able to complete these at a time tough, and it will depend on which faction controls the zone. Basically you have the zone with World Quests after you win the Warfront (after it has ran for 7 days), and keep it until the other faction successfully claims it as part of their Warfront scenario.
This means that you have between 7 and 12 days (for the most part) to do the daily World Quests before the other faction will recapture the zone and claim the daily WQs.
The only requirement to get to do these World Quests is that at least one character on your account has done the Tyrande 8.1 quest chain where you are awarded with the new eye options for Night Elf characters (the reward is obviously for Alliance only). This quest chain should only take 30 minutes to complete, and the portal from the main hubs to level 120 Darkshore won't appear until you have completed this one minimum one character.