The number of independent co-ordinates required to describe the motion of a system is termed as degrees of freedom.
For example Particle - 3 dof (positions) Rigid body-6 dof (3-positions and 3-orientations) Continuous elastic body - infinite dof (three positions to each particle of the body).
If part of such continuous elastic bodies may be assumed to be rigid (or lumped) and the system may be considered to be dynamically equivalent to one having finite dof (or lumped mass systems).
Large number of vibration problems can be analyzed with sufficient accuracy by reducing the system to one having a few dof.