It's to do with the dissociations.
If you take a diprotic acid, H2SO4, the dissociation equations are:
H2S04 -> H+ + HSO4- (very strong)
HSO4- -> H+ + SO4(2-) (weak)
The first step will ionise completely, whereas the second will not as removing a hydrogen would have to overcome the electro-attractive force between the negative ion and the H+.
The more hydrogens you remove, the harder it becomes to completely ionise it and the strength of an acid is related to its ability to donate an H+ .