A bodies motion is observed by relating a Frame of Reference to an observer, and measuring the positional change of the body, relative to the frame of reference with change in time.
The branch of physics that concerns an objects motion without regard to the cause of the motion is Kinematics, while the branch that focuses on the effect of forces on motion is Dynamics.
The concept of motion is relevant in many physical systems, and in general, can be considered to be a continuous change in the position or configuration of some physical system in Space.
Within the fields of Geometry and mechanics, a displacement is a vector, the length of which is the shortest distance from an initial, to a final position of some point P in Motion.
It also suggests that the Motion of physical systems are deterministic, meaning that a small number of parameters contain the importance parts of the history of the system, such that you can predict the future of the system.
Physics is often defined as the study of Matter in Motion. This is part of the reason that physics relates to the other sciences in the way it does: all other sciences observe that which is made of matter, and in motion.
Within the field of Classical Mechanics, Newton's laws of motion, are three laws which define the relationship between objects in motion, and the forces these objects are subject too.