Abbreviation: DX = "APS-C format for Nikon" (Nikon)

The abbreviations means "APS-C format for Nikon"

Explanation from Nikon

Nikon digital SLRs have either an FX or a DX sensor. The FX sensor, measuring 24x36mm, is roughly equivalent to the size of the 35mm film frame. The DX sensor is smaller, measuring 15.8x23.6mm. DX-NIKKOR lenses are engineered and optimized for use on Nikon DX-format D-SLRs and are designed to cover the smaller image area of the DX sensor. When a DX lens is mounted on an FX-format Nikon D-SLR, the camera’s DX-Crop Mode is automatically engaged, introducing a 1.5x magnification (cropping) factor.

See examples of effected products

Nikon AF-S DX 18-55mm f/3,5-5,6 G ED VR
Nikon AF-S DX 10-24mm f/3,5-4,5 G IF-ED
Nikon AF-S DX 85mm f/3,5 G ED Micro VR

See links

nikonusa.com