The Collaborative International Dictionary of English v.0.48:

resilience \re*sil"i*ence\ (r[-e]*z[i^]l"[i^]*ens), resiliency
\re*sil"i*en*cy\ (r[-e]*z[i^]l"[i^]*en*s[y^]), n.
   1. The act of springing back, rebounding, or resiling; as,
      the resilience of a ball or of sound.
      [1913 Webster]

   2. The power or inherent property of returning to the form
      from which a substance is bent, stretched, compressed, or
      twisted; elasticity[1]; springiness; -- of objects and
      substances.
      [PJC]

   3. Hence: The power or ability to recover quickly from a
      setback, depression, illness, overwork or other adversity;
      buoyancy; elasticity[2]; -- of people.
      [PJC]

   4. (Mech. & Engin.) The mechanical work required to strain an
      elastic body, as a deflected beam, stretched spring, etc.,
      to the elastic limit; also, the work performed by the body
      in recovering from such strain.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Elasticity \E`las*tic"i*ty\ ([=e]`l[a^]s*t[i^]s"[i^]*t[y^]), n.
   [Cf. F. ['e]lasticit['e].]
   1. The quality of being elastic; the inherent property in
      bodies by which they recover their former figure or
      dimensions, after the removal of external pressure or
      altering force; springiness; resilience; tendency to
      rebound; as, the elasticity of caoutchouc; the elasticity
      of the air.
      [1913 Webster]

   2. Power of resistance to, or recovery from, depression or
      overwork; -- usually referred to as resilience[3].
      [1913 Webster]

   Coefficient of elasticity, the quotient of a stress (of a
      given kind), by the strain (of a given kind) which it
      produces; -- called also coefficient of resistance.

   Surface of elasticity (Geom.), the pedal surface of an
      ellipsoid (see Pedal); a surface used in explaining the
      phenomena of double refraction and their relation to the
      elastic force of the luminous ether in crystalline media.
      [1913 Webster]

WordNet (r) 3.0 (2006):

resilience
    n 1: the physical property of a material that can return to its
         original shape or position after deformation that does not
         exceed its elastic limit [syn: resilience, resiliency]
    2: an occurrence of rebounding or springing back [syn:
       resilience, resiliency]