Too much of something
Over- always signals excess: more than normal, more than desired, more than correct. With verbs it means doing something too much: overeat, oversleep, overcharge, overload. With adjectives and nouns it signals something that exceeds the expected level: overconfident, overtime, overpriced.
Over- as "above" and "across"
Over- also has a spatial meaning: above or across. overpass = a road that goes over another; overhead = above the head; overall = across everything. "Overcome" literally means to come over an obstacle. In everyday conversation, the excess sense is by far the more productive meaning to learn first.