Adsense publishers can now specify a Whitelist or website URLs where the Google Ads should be displayed. For instance, if you enabled Allowed Site only for abc.com and use your Adsense Publisher ID to display ads on xyz.com, the Google ads will still display though you won't generate any revenue from the clicks or impressions.
Google probably introduced this setting to prevent cases of Adsense Theft where someone takes your Adsense ID (google_ad_client) and uses it on another inappropriate site. This has happened with us as well when a porn website was displaying Google ads using our publisher ID - Google quickly sent a warning email but the matter was resolved in few hours.
Are you planning to turn on the Allowed Sites option? As an Adsense Publisher myself, I'll probably leave that untouched mainly because a part of traffic coming to this site originates from Google/Yahoo cache (when the main site is inaccessible), online translation services like Babelfish (for non-English visitors) and from proxy servers (where the site may be banned). And some social sites / web directories display external content inside frames.
With Adsense Whitelist in place, you miss an opportunity to monetize this indirect traffic though the visitors will still see Google ads on your web pages, advertisers will be charged by Google but the Adsense revenue won't be shared with you.
If you are really worried that other illegal sites are using your Adsense publisher ID, you can easily detect that using Adsense channels.