Abbreviation: ASP = "Aspherical Lens" (Sigma)

The abbreviations means "Aspherical Lens"

Explanation from Sigma

The aspherical lens complex allows freedom of design, improved performance, a reduced number of component lenses and a compact size.

This lens provides high optical performance while maintaining a compactsize. For example, the 12-24 mm f/4.5-5.6 EX DG ASPHERICAL lens widensthe range of wide-angle lenses, and it provides distortion-free images withimage reproduction performance equivalent to that of a single-focal lengthlens. Aspherical lenses allow the production of high-quality images fromcompact, lightweight telephoto zoom lenses.

See examples of effected products

Sigma EX 24mm f/1,8 DG ASP Macro
Sigma EX 20mm f/1,8 DG ASP RF
Sigma EX 28mm f/1,8 DG ASP Macro

See links

sigmaphoto.com
sigma-photo.co.jp