Symbolism, Imagery, Allegory
Sure, everyone has eyes, but Count Olaf is most associated with the symbol of a single eye. Not only does he have an eye decorating his front door and a room filled with drawings of eyes, but he also has an ocular tattoo on his ankle. Check it:
They could see, in the space of pale skin between his tattered trouser cuff and his black shoe, that Count Olaf had an image of an eye tattooed on his ankle, matching the eye on his front door. They wondered how many other eyes were in Count Olaf's house, and whether, for the rest of their lives, they would always feel as though Count Olaf were watching them even when he wasn't nearby. (2.49)
Creepy, right?
While eyes can be symbols of good luck in some cultures (the ancient Egyptians had the Eye of Horus to watch over them and protect them), this one has some nasty connotations. Basically, the presence of this one freaky-looking eye makes the Baudelaires feel like Count Olaf is always watching them. Even though Count Olaf might not always be physically around, the children have the sense that he has his eye on their fortune… and on some terrible way to kill them once he gets his hands on that money. It seems likely they're right, too.
The eye takes on bigger significance in the rest of A Series of Unfortunate Events (you'll have to read on to find out how—no spoilers here). But for now, you can be sure that Count Olaf and his weird, ever-watching eye will be popping up again and again. Sigh.