What does "ship spinning" mean in EVE?

Before Captain's Quarters was added, docking at a station gave you a third-person view of your ship in a hangar, with the camera slowly rotating around it. You could also your mouse to spin the camera. Spinning your ship around was one of the most popular in-game activities for many players.

(In all seriousness, you'd probably be doing other things while docked like chatting, placing market orders, or refitting your ship, but it's a funny joke.)

Players did have some legitimate complaints about this feature's removal, however:

[...] As it turns out, [Captain's Quarters] didn‘t allow you to look at the ship from all angles, it requires far more GPU and CPU power than simply rendering a ship and a hangar and, importantly, we didn‘t retain UI functionality such as drag-dropping a ship onto your hangar to activate it or double-clicking on the ship to open its cargo. We know that it‘s annoying as hell logging into a station on a craptop trying to sort out some market orders and feel it slowly roasting your lap while it renders your pencil skirt-wearing Caldari commander lady.

It means your ship rotating when you're in the first person mode in your quarters.

In you quarters, you can only ever see one side of your ship. These users want to be able to see every side, by spinning it.