One dimensional motion is restricted to just a line. Thing about an object that can only travel on the x-axis. It's displacement, velocity and acceleration can be defined by just single numbers. The sign of that number can indicate the direction since there are only two directions.
On the other hand, two dimensional motion can happen on a plane. Think about an object that can travel anywhere on a Cartesian plane (normal graphing paper with x-axis and y-axis). This object's displacement, velocity and acceleration need to defined by two numbers and is done so usually in vectors. For example the position can be (3, 5).