The Coriolis-force (or Coriolis-effect) is a concept mainly used in meterology. It is an "apparent/virtual" force causing the air to form whirls circling "clockwise" in the Northern Hemisphere and "anti-clockwise" in the Southern Hemisphere. This effect is based on two different phenomena!
The Coriolis-effect affecting North/South motion is very easy to understand. Every point on the Earth surface moves towards east due to the rotation of the Earth. The velocity of this eastward motion for a point on the Earth surface is proportional to its distance from the rotational axis of the Earth. For a point at the Equator this speed is about 500 m/s (1800 km/hour), close to the poles this speed is (close to) zero. If you move in North/South direction and "cling to the Earth surface" your eastward speed is changed and the inertial reaction to this will be experienced as an east/west force that needs to be overcome. This is exatly the same as when you displace yourself in the radial direction on a "merry go round".
The Coriolis effect affecting East/West motion is a bit different!
Because of the Earth rotation the Earth has taken a shape such that the gravitational force acting on a surface point is not exactly normal to the surface but slightly tilted away from the equator! This tilt results in a horisontal force component with exactly the size required to prevent a mass element at rest on the surface of the Earth to start sliding away towards the equator. This is illustrated in the following picture
If a mass point moves in direction east relative to the Earth surface and its eastward velocity therefore is higher then for a point at rest relative the surface of the Earth the horisontal component of the gravitational force is not sufficient to counter-act the horisontal component of the centrifugal force and it will start sliding towards the equator. This will then appear as a force directed towards the Equator (due south in the Northern Hemisphere, due north in the Southern Hemisphere). If the mass point instead is moving towards west relative to the Earth surface the eastward velocity is lower then for a mass point at rest relative the surface of the Earth and the horisontal component of the gravitational force will be stronger then what is required to prevent the mass point to slide towards the equator and it will instead slide towards the pole (the North Pole on the northern hemisphere, the South Pole on the southern hemisphere)
The motion of a mass point over the surface of the Earth in any direction is a superposition of a north/south motion and an east/west motion. Both components of this motion causes an apparent "coriolis-force " as described above. The vector sum of these apparent horisontal "coriolis-forces " can be shown to always have a direcion orthogonal to the direction of motion and to have a magnitude independent of the direction of motion. In the northern hemisphere this apparent force is in direction "right" relative the direction of motion corresponding to a "clock-wise" rotation, in the southern hemisphere this apparent force is in direction "left" relative the direction of motion corresponding to an "anti-clock-wise" rotation