Core Gameplay Changes

Most of the mods that affect the core gameplay mechanics come from the excellent "Simonrim" Gameplay Suite.
I will try to give a brief overview of the larger changes.

New Skills

Skyrim’s skill trees have had a couple of pretty big changes. You should keep these new skills in mind when creating a new character.

Hand to Hand

Choosing to take perks in the Hand to Hand skill tree will give you bonuses related to…you guessed it…unarmed combat. Perks include bonuses to unarmed damage, movement speed when unarmed, stamina bonuses, and more.
This type of build was not really viable long term in vanilla Skyrim.

Security

Lockpicking and Pickpocket have been combined into a singualar skill called “Security”. Perks in this tree are a much better investment than they were before.

Security is the art of opening locks and picking pockets. Those who are skilled in Security can find hidden treasures, disarm an unaware target, and silently poison their foes.

Dragonborn

Dragonborn is a new perk tree thats not part of the main perk menu (think like there Werewolf perks or Vampire Lord)

Once you bring the horn back to High Hrothgar to complete your training, you will recieve a new power called “Meditate”. Using this power will cause your character to kneel to meditate, and the new perk tree will appear.

You acquire new perks for the Dragonborn perk tree by killing dragons and absorbing their souls.

These perks will give bonuses such as reduced shout cooldown, increased power, and more. Investing into this skill tree will enable your shouts to pack a harder punch.

Crafting Changes

In Winds of the North, there is a new type of crafting called “Scroll Crafting” and a major overhaul of Staff Enchanting (thanks to Sorcerer and Staff Enchanting Plus). Cooking has also recieved a major overhaul.

Scroll Crafting

Staff Enchanting

In vanilla, the staff enchanting system functioned sort of like a forge. You had preset recipes that you “crafted”. Sorcerer and Staff Enchanting Plus allows staff enchanting at the new tables to function like normal enchanting would.

Mage vendors can now sell unenchanted staves. You can take these staves and enchant them at one of the new tables placed around the game world.

Cooking

World Leveling

Arena

Even though Arena may seem inconspicious, it actually has a very large affect on the game’s difficulty and progression.
Mostly, its main direct changes is modifying the level of enemies via encounter zone and spawn difficulty multiplier changes.

What this means is that certain types of dungeons will spawn with enemies being a minimum level, and the difficulty of a spawn has a multiplier on top of that. There is a clear distinction between which type of enemies you can expect to be difficult vs not.
Simon words the end result much better than I can:

The result of these Encounter Zones is that the player is able to combine the freedom of an open world game with the progression you experience in a leveled one. If you’re level 8, you can walk into any Bandit dungeon and know that with good play and a few potions, you’ll be able to complete it. However, if you stumble into a Vampire den, you may want to turn around. However, once you’re closer to level 25, you’ll be able to return and complete the dungeon–in fact, by level 25, you’ll largely be equipped to tackle any encounter in the game.

0.75x: Easy
1.00x: Normal
1.25x: Hard
1.50x: Very Hard
Level 05: Bandits
Level 10: Draugr, Animals, Spriggans
Level 15: Mages, Forsworn
Level 20: Falmer, Dwarves, Giants, Dragon Lairs
Level 25: Vampires
Level 30: Dragon Priest Dungeons, Daedra

Survival, Inns, and Fast Travel

Inns

TODO - Screenshot of inn dialogue

Inns now function a little differently than you may be used to. You may now rent an Inn room for an extended amount of time. This can serve as a cheaper alternative to a home until you save enough to buy one.

One night (for 50 gold)
One week (for 250 gold)
One month (for 750 gold)

Inns in major cities, such as the Bannered Mare, Candlehearth Hall, the Silver-Blood Inn, the Winking Skeever, and the Bee and Barb charge more (75 gold for a night, 350 gold for a week, and 1000 gold for a month).

In addition, when you rent a room in an inn you will gain access to safe storage for that duration of the rental.
When the rental expires, the chest will simply lock and your goods will remain safe inside. To get your items back you can renew your stay and everything will still be there.

Fast Travel

Rather than being completely disabled, fast travel now requires a “Travel Pack”.

TODO-Screenshot of travel pack

Travel packs can be crafted from any blacksmith’s forge, purchased from general merchants, and found occasionally in “clutter” type loot.