I think Sauron having his external image as an eye did two things to his servants:
1. As
Galadriel said, it was a constant reminder that he was there and watching them, especially when the Eye was used as a device on shields and whatnot as well. It was like the Big Brother image in
1984: there was no escaping it for Mordorians.
2. The Eye image would also be a means of making Sauron seem impersonal, a desirable trait for one, like him, who desired to be considered not only a king but also a god to his people.
Here is another thread from a while back that deals with the same subject and has some excellent points.