The beam is supported at C by post (1). As load w is applied to the beam, a portion of this load is transmitted to the support post.
The reaction force causes the post to contract (i.e., the post gets a little bit shorter). Unlike a rigid support, the axial deformation of post (1) allows the beam to move downward at C.
How much will the beam deflect at C?
We don't know the exact value at this time, but we do know that the beam deflection at C will be exactly the same as the contraction that occurs in post CD.