Think of it like this, the particle is feeling the force on the side, it makes it turn (but the velocity will not change). So now consider the same particle in a new point in the system, your particle has turned for a little bit, and now still feels the force on it's side, which will make it continue to turn.
Now do this for all following points that exist in it's path, and you will see it will continue to move in a circle.
As the diagram says, the force is always perpendicular to the direction it's moving.
Think of a centripetal force, if that makes it more easy.