A nonholonomic system in physics and mathematics is a system whose state depends on the path taken to achieve it. Such a system is described by a set of parameters subject to differential constraints, such that when the system evolves along a path in its parameter space (the parameters varying continuously in values) but finally returns to the original set of values at the start of the path, the system itself may not have returned to its original state. e.g. A robot is holonomic if the controllable degrees of freedom are equal to the total degrees of freedom.

For a very good example refer to this paper:

Flash, Tamar ; Meirovitch, Yaron ; Barliya, Avi (2012). "Models of human movement: trajectory planning and inverse kinematics studies". Robotics and Autonomous Systems (Elsevier).