First off, cork is a good choice from an environmental standpoint.  It's harvested from sustainable sources, mostly around the Mediterranean in Europe.  As an interesting aside, the increasing use of plastic wine corks has been threatening the cork production industry, so you could actually help keep alive an age-old industry by choosing a cork floor.

(Source: Flooring Handbook)

Cork usually comes in tiles or planks of various sizes.  Because the material is lightweight and easy to cut, installation is usually uncomplicated and hassle-free.  

One of the benefits of cork is that it is great at absorbing sound.  It's also warm and comfortable to walk on, in contrast to wood, which is hard and cool underfoot.  Cork is soft, so if you drop something on it, it will dent, but because it's resilient, the floor will soon bounce back to normal.  

A downside of cork floors is that they aren't as durable as hardwood or even resilient floors like vinyl and linoleum.  It's prone to scuffs and scratches, so it won't last too long in high-traffic areas.  The life expectancy for cork flooring is about 5-10 years, though it'll last longer in low-traffic areas.  So, like carpet, it's not a permanent flooring solution.

Cork works particularly well in children's rooms (it's softer and warmer to play on than wood or laminate, and its resiliency lets it survive the dents caused by toy droppage), and it's also an increasingly popular choice in bathrooms.  Cork is a non-slip material, and it's comfortable under bare feet.  However, it needs to be sealed or the tiles/planks it comes in will absorb moisture that could make the seams swell open.  You can get "ready-sealed" tiles, but it's still a good idea to apply a coat of sealant to the whole floor once it's laid.

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