AdBlock Plus uses two methods, depending on your device/setup:
For non-root on modern Android with certain devices, it changes the network proxy settings.
For root devices, it uses the classic hosts file loopback trick which alters the DNS lookup. (Instead of returning the real IP address for www.some-ad.com it returns the local loopback IP, which won't return the ad.)
Either way, at the OS network level the network settings the ad blocker changes causes Android not too request the ad at all, but instead sends back an empty or dummy HTTP response to the app.
Since the ad request was never sent, the ad networks can't track you and of course then can't show an image or ad.
See more details on the AdBlock FAQ.