Explain why the gem-dimethyl groups appear as separate peaks in the proton NMR spectrum of isoborneol although they almost overlap in borneol.

We are talking about the difference between the structures of borneol and isoborneol (see the structures of both compounds in the link referenced below).  Both are bicyclic molecules with the norbornane structure at their cores.  The gem dimethyl group in question is the carbon at the top of the structures with two methyl (CH3) groups attached to it.  The only difference between the two molecules is the spatial orientation of the hydroxyl (OH) group.  In borneol, the hydroxyl group is pointed down and away from the gem dimethyl group.  In isoborneol, the hydroxyl group is pointed up and toward the gem dimethyl group.  Since NMR distinguishes between chemically unique hydrogen atoms, the hydroxyl group in isoborneol affects the methyl group that is pointed toward it but not the methyl group pointed away from it, thus the two methyl groups appear as two different peaks in the NMR spectrum.  In the case of borneol, the hydroxyl group is pointed in the opposite direction and therefore exerts essentially no effect on the gem dimethyl group, thus it appears as a single peak in the NMR spectrum.