The pitcher's mitt is a brown baseball glove, not to be confused with the green climbing gloves.
The pitcher's mitt increases the speed and flattens the trajectory of thrown objects, allowing light objects (such as rocks and pots) to be hurled much farther, and making heavy objects (such as chests and Idols) more practical weapons.
A secondary effect is that if you throw an item which rebounds and hits the Spelunker, he will catch it instead of taking damage.
The pitcher's mitt doesn't impact the way bombs are thrown when using the bomb shortcut key, but does affect their distance when the bomb is equipped with the C key and then thrown with the action button.
Using a pitcher's mitt to throw an arrow into any wall tile (but not stone and push blocks) will stick it into the tile, thus allowing you to grab onto it as you would a ledge, a feat that can otherwise be accomplished only by shooting the arrow with a bow or performing a running throw.
The pitcher's mitt can be equipped along with the climbing gloves, allowing for both effects at once.
Cheating the Dice House
If you throw a die with the pitcher's mitt equipped, you will notice that you'll be able to catch the die flying before it finishes rolling on the shop floor: The end of the throwing sequence - when the result of the throw is already decided - will be in a sort of slow motion, allowing you to catch the die and re-roll it without angering the Shopkeeper.
With a little timing and patience this may allow you to earn huge amounts of money and prize items.