This skill determines how well a character can use sneak mode to sneak around NPC's. If you do manage to sneak up on a character and then attack them, you have a chance at a critical hit. To tell whether or not you are visible, when sneaking and undetected there is an icon near the bottom. This icon displays the skill symbol for Sneak, a hand reaching for a bag. If the icon isn't present, then you have been detected.
If, when sneaking, you activate an NPC, a portion of their inventory is shown, and you may attempt to pickpocket them. If they notice you trying, however, it is considered a crime, regardless of whether you took anything or not. It is interesting to note that if you exit their inventory and then activate it again, there may be different items present from before. The higher the sneak skill, the more items are shown.