It doesn't exactly occupy more space, but it has a different
shape to a bond pair. In a bond pair we have two positive nuclei,
with most of the density of the bonding electron pair between the
atoms. The outer nucleus attracts the bond pair outwards from the
central atom. In a lone pair there is only the central atom to
attract the electrons, so they are pulled in more than the bond
pair, producing a fatter, squatter shape. This means that more of
the electron density is near the central atom than with a bond
pair, which makes it more effective at repelling the other electron
pairs. Thus there is a difference in the amount of repulsion
between different sorts of pair, meaning that he angles between
them are different too, in the order, from greatest to least, lone
pair-lone pair, lone pair-bond pair, bond pair-bond pair.