A bridge is structure carrying a pathway or roadway over a depression or obstacle. They are built to connect two points separated by a naturally occurring region like valley, river, sea or any other water bodies, etc.
An overpass on the other hand is the upper level of a crossing. It's a bridge or crossing of two highways or of a highway and pedestrian path or railroad at different levels where clearance to traffic on the lower level is obtained by elevating the higher level.
Understand some of the history behind bridge building, read amazing information related to suspension bridges, arch bridges, beam bridges and more at Science Kids.