An eye in the middle of a symbol is in almost cases referred by as "all seeing eye". This is a symbol of early Christian, to show the eye of God, watching over humanity (Wikipedia "Eye of Providence")
If I assume the background are three moons with points of intersection (see the picture), then this three are the symbol of "Triple Crescent Moon". Like this website wrote: a symbol for three stages of women life, or in general three fates (birth, life and death). And it should be the opposite to the horned god.
Strange thing: If one search for pictures with "symbol triple crescent moons" one gets some of biohazard as jewelry too...
Like I wrote in my comment: The three outer circles in biohazard symbol do touch, but have no point of intersection. The symbol on Moody's clock clearly have outer circles with point of intersection.
So it is not the biohazard symbol, but the similarity is intended I assume, to illustrate the role of Moody as an Auror, who watch over the "normal" people (magic and non magic) to find the evil and guard them against it. "Magic-hazard", if you want to call it that.