Prestressed concrete is concrete where an internal stress has been introduced to put the element into compression. Tensile bending stresses due to self and applied loading are then offset by the inbuilt compression.
The prestress is introduced by tensioning steel within the concrete either before the concrete is cast (pre-tensioning) or after casting in which case ducts are cast into the section and steel tendons are then passed through the ducts, tensioned and anchored putting the concrete into compression (post-tensioning).
In reinforced concrete, reinforcement in the form of steel bars or fabric (or FRP bars or potentially specialist fibres) is placed in areas where tensile stresses will occur under load. The reinforcement is strong in tension and is able to absorb the stresses developing in the concrete so long as a good bond between the concrete and steel is maintained. By limiting the stresses that the steel has to deal with, the cracking in to concrete can be kept with-in acceptable limits.
In prestressed concrete, the compressive stresses introduced into areas where tensile stresses develop under load will resist or annul these tensile stresses. So the concrete beam behaves as if it has a high tensile strength of its own. Provided the tensile stresses do not exceed to pre-compression stresses, cracking cannot occur in the bottom of the beam.