In Tamron-land, Di stands for "Digitally integrated", and basically it means the glass elements in the lenses have differet coatings to give them better anti-flare problems. (That is considered to be useful for digital cameras because you get more reflection off a sensor than off a film, hence more risk of flare.) However, mechanically and optically they are identical to the earlier "non-Di" lenses, and they can be used on film SLRs as well as digital.
Tamron Di-II lenses are smaller, like Canon EF-S or Nikon DX or Sigma DC lenses, and only work with digital SLRs that have "cropped" sensors.