Every day when you log in, there is an emissary that asks you to do specific sets of world quests to aid a faction (eg all Dreamweaver faction quests in Val'sharah). Do four quests for the emissary and get an awesome chest. These emissary quests kind of work like Hearthstone dailies - they pile up for a few days, so you can catch up on ones you missed.
Legion will still have dailies, though these "world quests" seem more similar to Diablo 3 bounties. But they're adding a bit of a buffer, allowing you to save quests for a few days.
The leveling-up experience in classic zones is pretty broken right now and not well tuned. It's way too easy and it was neglected for a bit. Due to ability changes over the years, you basically feel invincible (even before heirlooms). You're running around more vs actually fighting. The pacing of the game isn't what it should be. They've been looking to fix this (even via hotfixes now).
As I remarked a few weeks ago, leveling is excessively easy with a very fast Time-to-kill. It's good to know that it's on Blizzard's list of things to fix.
As an aside, it's not all classes which are broken. I've been leveling a human Fire Mage, and that specialization feels surprisingly right while leveling. Admittedly, I'm only in quest rewards with no dungeon gear or heirlooms. Perhaps that spec is just under-tuned. It might be a function of not having enough critical strike, as Fire seems to want more critical strike rating to get off instant Pyroblasts. But I actually took First Aid to make bandages to keep my health up. Given my experience leveling a druid, that was completely unexpected.
In any case, there's a decent amount of interesting information on the major system changes coming in Legion. So far, it all sounds pretty good.