I read on Wikipedia that 2,3 BPG binds with the deoxygenated state of hemoglobin and helps in stabilizing it. It was also written that it helps release remaining oxygen from the hemoglobin. How?
You've answered your own question. The association/dissociation of oxygen is an equilibrium reaction. If you stabilize one state, you move the equilibrium to that state. 2,3-BPG helps release oxygen from Hb exactly by binding and stabilizing deoxy-Hb.
From more mechanistic point of view, 2,3-biphosphoglycerate contains 2 negatively charged phosphate groups, which interacts with positively charged groups of each beta-chain within deoxyhaemoglobin decreasing the oxygen affinity (see good old Stryer Biochemistry)