Ship spinning is docking in a station and rotating the camera around your ship
When CCP introduced "captain’s quarters", the “hanger view” was removed and many people were upset with the loss of spinning the camera around a ship in station.
CCP not only reintroduced the “hanger view” to allow ship spinning, but added a ship spinning counter. If you spin your ship over 10 times, the number is shown in grey at the bottom center.
When the counter reaches 1000, 2000, 3000 etc, the number briefly flashes blue.
Ship spinning trick: you don't have to rotate in the same direction. you can actually just hold down the left mouse button and shake the mouse left and right. The farther left and right you shake the quicker the counter goes up