If you have stacked items (more than one of the same thing) in a bag and you use the 'split' feature, it will split the items.

The split items however DO NOT GO INTO YOUR INVENTORY. They instead DROP AT YOUR FEET.

I just had this happen with a pair of stacked Bulls Strength in a regular leather bag. I hit split and I thought it vanished, but when I backed up, it was lying at my feet.

I think it's meant to be used in the following situation.

3 spunky adventurers are out spelunking (as adventurers do) and find a stack of 3 major healing potions. Well one picks them up and would like to quickly share them with his fellow spelunking adventurers. He uses the split function to drop one at his feet, takes a step, and splits again. This allows the other two to quickly pick up their things without the worry of using the trade window.

Likely this is just yet another issue with containers. Splitting usually sends one part to the first empty space of inventory that can hold the item. If there's no room for the item in any inventory tab, the item is dropped.

I tend to agree with Snoteye. But still it's worth noting that it does not go from your pouch/bag/box into your inventory, but rather onto the ground.