Why does the structure of haemoglobin change when the ferrous ion changes to ferric ion?
The $\ce{Fe^{II}}$ ion is held in the centre of the heme's porphyrin ring and is also attached to a nitrogen atom on a nearly histidine group which is part of the protein. When there is no oxygen present the Fe ion is in a high spin state. The Fe has two electrons in the $e_g$ orbital and is 5 coordinate. The other 4 bonds are to the porphyrin N atoms making the geometry square pyramidal. In this state the Fe is just a little too big to fit into the porphyrin ring which becomes a distorted, bending towards the histidine. The Fe is 0.07 - 0.08 nm out of the plane and the Fe-N distance 0.22 nm (to the imidazole N on histidine F8). When an oxygen molecule binds the Fe becomes low spin, (the $e_g$ orbitals are now empty) and 6 coordinate, and  has a slightly smaller radius and so fits into the porphyrin ring which becomes planar. As the Fe has moved on binding oxygen, the histidine is also moved and is pulled towards the porphyrin ring by $\approx$ 0.075 nm. This motion is transmitted and amplified through the protein to the other three binding sites which affects their ability to bind. This is called an 'allosteric' interaction as it is 'non-contact' between the sites.
The picture (b) is self explanatory. The structure (a) shows the protein backbone as cylinders and the porphyrins and Fe at atoms. The Fe is yellow.

(Picture from 'Protein Physics' A. Finkelstein &amp; O. Ptitsyn, publ. Academic Press.)