This is a Terraria-level update. I don't know how to prioritize things, so here's a quick overview of the new hotness in the order in which Hello Games presented them.
First up, the graphics have been significantly overhauled, with better textures and lighting effects. The PS4 Pro can take advantage of new features and shinies.
Other players' bases can now be found and explored, and Steam Workshop will let you find them more easily.
YOU CAN NOW OWN MULTIPLE SHIPS OMG THANK YOU HELLO GAMES
Speaking of ships, each ship type has a clear specialization for combat, hauling freight, and exploration.
Multi-tools also have specializations, for mining, combat, and scanning.
Ships and weapons now have classes: A, B, C, or a rare S-Class.
You can now build ground vehicles called Exocraft for getting around on-planet. There are three classes of these for speed, hauling loot, or somewhere in the middle.
You can make Exocraft races and challenge others to beat your time!
There are new traders in space stations, some of which sell blueprints that you can buy with a new currency: nanite clusters.
Base-building now has way more options so you can pimp out your house in style!
Multi-tool and ship weapons have far more variety now, for close-, mid-, and long-range combat.
There's a new game mode: permadeath. If you were ever playing NMS and thought "I wish I could lose all this when I die," then this mode is for you.
There are five new trophies for claiming a base or freighter, building an exocraft, visiting another player's base, and reaching the center of the galaxy in Survival and Permadeath mode. Those last two should take a while.
There's now a dedicated photo mode so you can stop time and line up the perfect shot! You can choose the time of day and lighting effects and add photo filters.
The Discovery menu has gotten some significant updates; it's actually useful! You can find yourself and set waypoints to previous systems.
65daysofstatic has created 8 new soundscapes for that awesome procedurally generated soundtrack.
You can name your ships now.
You can skip those annoying black bar cutscenes.
NPCs are faster at getting to the point when you talk to them.
And various other improvements.
For the full list, check this post from Hello Games: http://no-mans-sky.com/pathfinder-update/