Abbreviation: XR = "Extra Refractive Index Glass" (Tamron)

The abbreviations means "Extra Refractive Index Glass"

Explanation from Tamron

XR (Extra Refractive Index) glass can bend light rays at steeper angles, thereby decreasing the physical length of the lens while enhancing imaging performance by minimizing optical aberrations. This has allowed Tamron to develop a line of shorter, smaller-diameter, lighter lenses without sacrificing lens speed, and actually upgrading image quality compared to older designs. XR glass is costlier than conventional glass but it yields enhanced optical power distribution, making possible many of the outstanding and innovative lens designs that bear the XR designation. XR glass, with its superior light-bending power, makes it possible to design a short-barrel lens with the same light-gathering ability (aperture value) as a long-barrel lens—even with a smaller lens diameter. By using this principle Tamron has been able to shorten the length of the entire optical system and produce lighter, more compact lenses of the same speed, and also to provide greater zoom ranges in lenses that are much more convenient to carry and hand-hold.

See examples of effected products

Tamron AF 18-200mm f/3,5-6,3 XR Di II
Tamron AF 18-250mm f/3,5-6,3 XR Di II
Tamron SP AF 17-50mm f/2,8 XR Di-II LD Asph IF

See links

tamron-usa.com