It is reversable as the haemoglobin can "pick up" oxygen to become oxyhaemoglobin, and then can give it up to become haemoglobin. This is how oxygen is carried through the body.
Haemoglobin can absorb other substances such as carbon monoxide causing it to become caroxyhaemoglobin. This is not reversable so will remain as caroxyhaemoglobin, which is how carbon monoxide can kill a person by using up all the haemoglobin.
(I hope this is correct as it is from memory - and is from the Human Biology A' level that I passed in 1979)