If we are talking about the Cartesian coordinates system where coordinates are represented by (x,y,z).
Then depending upon how many coordinates are used to describe the motion of an object, there are 3 types of motion.
One Dimension (1-D) Motion-
If only one coordinate is used to describe the motion of an object.
Motion along a straight line is an example of is 1-D motion
E.g: Train running on a single track, Apple falling from a tree
Two Dimension (2-D)-
When two coordinates are used to describe the motion of an object.
Motion in the plane is an example of is 2-D motion
E.g Earth revolves around the sun.
Three Dimension -
When all the three coordinates are used to describe the motion of an object.
The motion in space is 3-D motion.
e.g: object moving in space randomly.