Abbreviation: APO = "Apochromatic" (Sigma)

The abbreviations means "Apochromatic"

Explanation from Sigma

In order to attain the highest quality images, the APO lens has been made using special low-dispersion (SLD) glass and is designed to minimize color aberration.

SIGMA“s APO zoom lenses minimizecolor aberration. As the refractiveindex of glass depends on thewavelength of light,color aberrationoccurs when different colors formimages at different points. Thisproblem often occurs with telephotolenses,but the Special Low-Dispersion(SLD) glass and Extraordinary LowDispersion (ELD) used in SIGMA“sAPO lenses helps to compensate forcolor aberration, thereby allowingthem to produce of sharp images.

See examples of effected products

Sigma EX 50-150mm f/2,8 II DC APO HSM
Sigma EX 200-500mm f/2,8 APO HSM DG
Sigma EX 70-200mm f/2,8 II APO HSM DG Macro

See links

sigmaphoto.com
sigma-photo.co.jp