Anion exchange chromatography aims at separating and retaining anions, or negatively charged particles, by using a positively charged absorbent functional group.
The same principle I described for cation exchange chromatography applies here, i.e. like charges repel and opposite charges attract.
In the case of anion exchange chromatography, the positively charged stationary phase particles will separate and retain the negatively charged proteins.
Here's a nice image I found showing the anion-exchange chromatography process
Notice that the anions bind to the positively charged static phase particles; at the same time, the positively charged proteins go through without being retained.