In the context of physics and applied mathematics, a body is an object (possibly idealized) which is imagined to have a material existence in the physical universe.
A body can be considered as an aggregate of particles to which it is possible to apply a force.
A rigid body is a body $B$ with the property that the distance between any two points of $B$ remains constant regardless of any external forces.
A deformable body is a body $B$ which is not rigid.
That is, when under the influence of a force, the distance between any two points of $B$ may not remain constant.