Tensile capacity of concrete is generally neglected during RC design. One the opposite side, one could (in a non-realistic way) consider that concrete beams deflects without cracking, leading to a full tensile capacity of the concrete. Tension stiffening effect is nothing more than concrete ability to carry tensile stress between adjacent cracks, in a kind of average behaviour between uncracked and cracked states. This is mainly due to transfer of forces from the steel reinforcement to concrete through bond.
Please refer to "R. I. Gilbert, Tension Stiffening in Lightly Reinforced Concrete Slabs, Journal of Structural Engineering 133(6), 2007", where the author presents a review on the concept and the main design guidelines addressing it. @R_Gilbert