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?
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)
If I understand your question, you want to know, HOW the 2,3-biphosphoglycerate helps release the oxygen from the heme. In addition to other factors like the blood temperature, the pH, and the ambient pCO2, it modifies the heme oxygen affinity. It binds, using salt bridges to lysine and histidine of deoxygenated heme subunits and, by this, changes the deoxygenated heme's conformation. The so modified heme conformation renders the (oxygenated) heme-oxygen bond instable. The altered heme subunit conformation cannot hold the oxygen atom anymore, which dissociates from the heme subunit and diffuses to the mitochondria, thus allowing for ATP production. This process is called "the hemoglobin oxygen affinity is being reduced" and one of the promoting factors of this process is 2,3-DPG.