A joystick can be moved in a direction (x and y axis) and some of them can also be turned (the z axis). A digital joystick gives only a on-off state for each off the cardinal directions so a maximum of eight directions is possible. Digital joysticks was the common game controllers in arcade games and home computers in the 1980's but they have now mostly been replaced by directional pads.
A analog joystick return a position along each axis, for example between -32768 to 32768. Negative values signify down or to the left. The game needs to manage a dead zone in the center that is seen as no movement.
Besides the stick itself a joystick also have buttons.