What do "two dimensional motion" and "three dimensional motion" mean?
It comes down to whether the path of the moving body lies in a single plane or not.
In two-dimensional motion, the path the object follows lies in a plane.
Examples are projectile motion where the path is a parabola, or planetary motion where it is an ellipse.
Three-dimensional motion would be a case where the path is more complex and is not confined to a single plane. A example would be the flight of an airplane or a boomerang.
By the way, there is also one-dimensional motion where the object follows a single straight line, like a free-falling object.