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A niche in the wall of a mosque. It indicates the qibla, the direction facing Mecca, and therefore the direction that a Muslim should face while performing salat, the five standard daily prayers. It is also where anyone leading a prayer would stand, and is basically the center and focus of all prayer in the mosque. A mihrab is usually well-decorated, and is often the most ornate part of the mosque. The mihrab is thought to be inspired by features of Christian churches, and is believed to have first been introduced to Islam in the eighth or ninth century A.D. (the second or third Islamic century.)
There is a beautiful and striking mihrab installed in New York City's Metropolitan Museum of Art, in the Muslim art section's "Art of the Mosque" room. Reading about it today on its nearby plaque, I wondered if it points towards Mecca. By my reckoning, it points towards the Central Park side of the museum, roughly west. It seemed to me like it wouldn't be very respectful to take such a thing, install it in a museum, and have it point in the wrong direction, but then I wondered; when you're halfway around the world from a place, can you really say that it lies in one direction and not the opposite? After all, they didn't point it north or south.
By the way, I suggest that anyone visiting the Met stop in that particular room. In addition to the mihrab, they have an enormous Koran with beautiful gold calligraphy, and several other equally beautiful decorative elements of mosques.
Sources:
-The Metropolitan Museum of Art.
-The Encyclopedia of the Orient; http://i-cias.com/e.o/
-Britannica.com