The Wakhan Corridor (وخان in Persian) is the little panhandle of Badakhshan Province in the far northeast of Afghanistan, wedged between Tajikistan and Pakistan, and its only link to Xinjiang in China.
This is the area popularized in the recent book Stones into Schools, the follow up to Three Cups of Tea. Both of these books describe the work of the Central Asian Institute and the work of Greg Mortensen, the mountain-climber turned school builder. Both books are highly recommended and are largely responsible for his recommendation for consideration for the Nobel Prize for Peace (which he did not get, however).
Flora and fauna
While it may seem tempting to cross into China or Pakistan from this area, it is highly illegal and you stand a good chance of ending up in jail. The only legal way in and out is via Ishkashim, crossing the Oxus from the north (Tajikistan) or through the main body of Afghanistan (unstable)
Recently there has been word of a possible new border crossing between Afghanistan and Pakistan at the Broghil Pass. There aren't checkpoints as such, but if you're willing to do a lot of legwork to get the necessary and arduous permissions, start your enquiry in Kabul.
Alternatively there are some organisations such as Secret Compass  that arrange expeditions to the Wakhan, usually in the summertime.
You can hire a Jeep. A Jeep from Ishkashim to Sarhad-e-Wakhan (8-hour trip) cost $400 in June 2011; to Sarhad-e-Broghil, the price would have been $200. Getting back down from the valley can be difficult if you haven't arranged for a pick up, as traffic is very scarce.
Trekking is the main reason you would come to this region.