Stealth is the ability to move and act unseen or unnoticed. It involves both sticking to the shadows as well as adapting to your surroundings to act in a manner that won't draw attention to yourself, effectively hiding in plain sight. If you plan on doing any scouting, spying, elusive game hunting or less-than-reputable acts such as burglary and picking pockets, stealth is a must.
When attacking or sniping from stealth, the target has a chance to make a perception skill check and see the attack coming. The more badly they fail this check, the lower their maximum defensive roll will be. If they fail outright to see the attack coming, their defense will be a flat 0! Thus, stealth can be an extremely effective means of offense in the form of reducing the target's defenses. You can tell how surprised a target is by the presence and color of the (!) in the attack messaging, just before the attack rolls.
Example: You throw a punch at an animated training dummy! (!) (M: 152 vs D:68)
The color of the ! determines how surprised the target was: Green = very surprised, Yellow = moderately surprised, Brown = barely surprised. If they weren't surprised at all, the ! will not be present. In the case of sniping, this means they may now know your position, and you should unhide and then hide again if you want to continue sniping at them unseen.