A hoof pick is any device that's used for cleaning the underneath of a horse's hooves.
A horse's hoof has two pits on either side of the frog that can collect dirt and even foreign objects. Shod horses can also get foreign objects caught between the edge of the shoe and the hoof. It's very important to clean out the hoof so that these objects don't bruise the horse's sole.
There are three different kinds of hoof picks in common use:
1. The traditional hoofpick is made of metal or plastic and has a loop and then a hook at the end. Metal hoofpicks are more expensive, but tend to last a fair amount longer.
A traditional metal hoofpick (Image source: BLW). As you can see, it's been used a fair bit. The loop is the handle.
2. A hoof pick and brush combo, as can be seen at this link: http://www.victorycanter.com/Horka-Glitter-Hoof-Pick.html?gclid=CM2Li__F1L4CFQKhOgodNFoAjQ. This is the most popular kind of hoofpick in modern America. The brush on the other side has very stiff bristles and is used for removing dirt and mud from the hoof.
3. A folding hoofpick, as seen here: http://www.chicksaddlery.com/page/CDS/PROD/2500/FPK95?utm_source=shopzilla&utm_medium=cpc&utm_campaign=shopzilla%2Bdata%2Bfeed. Trail riders carry this kind - there's no risk of the pick end causing injury if you fall and it fits neatly in a pocket.
The pick is always used from the rear of the horse's hoof to the front to avoid poking the frog.