TL;DW:

• persistent hangars are instanced locations assigned to your home planet
• size of persistent hangars is based on the biggest ship you own (assigned on first login or patch reset)
• you’ll be able to keep things around, invite people etc
• you fly into the hangar via ATC as usual
• you can request anything in your inventory to be sent up in the cargo elevator and put it anywhere
• you can decide on the placement of items placed on the cargo elevator when requesting them
• some items will have to be put in cargo container when requesting
• item bank is a separate kiosk, used to request personal items (clothes, weapons etc)
• item banks are available in hangars and around hubs (LZs, hospitals, rooms)
• no more interacting with local inventory from anywhere
• ASOP terminals will be available inside the hangars, can request your ship from there
• ships are delivered via ground elevator in the middle of the hangar
• you can spawn ground vehicles as well
• you can spawn multiple ships at once (first one has to be moved away)
• you can fall into the ship elevator and die
• hangar sizes had to increase to fit everything needed for the new system
  • extra large: ~25% larger
  • large: ~30% larger
  • medium: the same but taller
  • small: hasn’t changed
• some small ships were reclassified to use larger hangars
• automatic (un)loading still exist as an option in the commodity terminal
• automatic (un)loading costs money
• ship has to be stored to make use of automatic (un)loading and will be locked for the duration of this process
• transfer times will vary by location (ex. cargo facilities will be faster)

Edit: added info about hangar size updates.