A lot of things have changed in Final Fantasy XIV: A Realm Reborn. Since many players come back for Heavensward, and they're shocked to find that the amount of differences from an already polished game launch to now. Here is a short and easy primer to understanding the core differences since launch, at least things that have directly impacted me returning to the game from my personal experience. A lot of random small changes have made it into the game, but many of them are small quality of life changes or additional story / dungeon content, which are less notable with Heavensward's launch. This is perfect if you're asking what have you missed in the game or if you're starting out and want to know what was added from the last time you looked at jumping in. This doesn't include what's new in Heavensward - that's an entire expansion that's new with a bazillion new pieces of various content.
Make Your Favorite Outfit
Through the use of glamours you can have your perfect outfit. If an item says "projectable" then you can use a glamour (purchase off the auction house or craft yourself) to put one item's apperance on another item. To use glamours, you must be level 50 and complete a quest.
Daily Roulette & Challenge Log
The daily roulette is a godsend that lets you get through your story missions on any characters by granting leveling characters huge XP rewards and high level characters currency (Allagan Tomestone of Law). You no longer have to wait forever for a group of like minded adventurers to join a low level party, queues usually take seconds even for DPS.
The challenge log is a weekly resetting "hunting log" that grants % of your EXP needed to level for doing things like dungeons, guildhests, etc. There is the sightseeing log, available to level 50 players, which lets you solve riddles which was added as well.
Oh and you can auto - skip cutscenes to make roulettes easier.
New Class & Jobs Available
The Rogue class was added in 2.4 along with the Ninja job. Heavensward added three additional classes, the Dark Knight, Machinist, and Astrologian. The Rogue only requires you to reach level 10 of one class and complete your level 10 class quest (and have the armory system unlocked so you can switch classes). The HS "extra jobs" require you to be level 50 and have unlocked Heavensward content.
Tons of Additional Story Content & Dungeons
The main story continued each patch and then some and a plethora of dungeons were added. With Heavensward, this doesn't mean you'll skip them, because many of them are tied to your main story quests that you must do. Worry not, with Heavensward, if you've never done a dungeon before then you'll be put on top of the list to get into that dungeon and the dungeon roulette should swing and pick that dungeon for you (the trade off being you don't get the roulette's XP). The coil was expanded on and the Crystal Tower was released with all of its parts, but this is less relevant now obviously as players move into Heavensward raid content.
A featured added before WoW garrisons were a thing, you can send your retainer out on various missions to bring you back loot. You assign them a class (they have a level cap equal to at or near the level of the equivalent class you have) and can equip them with gear and the such. They can then run out and get you valuable loot and crafting materials. Guildleves, beast tribe quests, and exchanginge 1,000 company seals for five give you the Venture coin you need to send your retainer off on these adventures.
Golden Saucer & Chocobo Colors
You can feed your chocobo to produce any kind of color Chocobo you'd want and, in addition to that, the Golden Saucer is in FFXIV which a series of mini-games for you to play.
Housing - Personal & FC
Players can own a house and Free Companies can own a house and players can own a personal room within a Free Company house. Housing isn't instanced, it's persistant, although broken into various wards. You might not find any houses for sell on your server, as they're very limited, and very expensive, but it's an interesting and neat feature. You can view housing on your server in one of the three housing districts attached to the main cities.
Random Other Updates
1. Echo Buff: In various dungeons, you can receive the echo buff for each wipe, making older content easier to achieve once it's past its prime.
2. Dungeon EXP: Massively increased to make dungeon kills worthwhile. Consider 1k EXP a kill when you need 300k to level.
3. Class Changes: Warriors are useful, compared to launch, and most classes are balanced.
4. Hildibrand Manderville: His quest line continued from 2.1 and on, if you want to go for the side quest fun.
5. All the Currencies: There is a bazillion ways to earn currencies, like Hunts that give allied seals, to tombstones, to beyond. Way too many updates related to obtaining gear to talk about, but needless to say, ARR gear comes in spades.
That's about all the really important updates that have affected my gameplay. There is a ton more you can dig up in the update archives, but this is about the most important things you need to know to get back to playing! Now go out there and save Eorzea.