What makes bridges so strong?
Concrete, steel, and geometry.
There are many kinds of bridges, and as many ways for them to be strong.
Suspension bridges, like the Golden Gate Bridge in San Francisco, get their strength from steel and geometry. The bridge is mostly in tension, the forces on it try to pull it apart more than they try to compress it. Steel has very high strength under tension, so steel cables are used to build the bridge. The towers supporting the bridge are under compression, and are made of steel, sitting on enormous concrete piers.
Other bridges are often made using arches of concrete. Concrete has very high compression strength, and an arch is almost entirely under compression instead of tension. This is due to the geometry of the arch, which channels the load downward into the ground.
Most smaller bridges, such as those used for freeway overpasses, use a trick that combines the tensile strength of steel with the compression strength of concrete. Reinforced and pre-stressed concrete are building techniques where steel reinforcements are added to concrete where it will be under tension. Little or no reinforcing is needed where the structure is only under compression forces . In a bridge span, the steel will be on the bottom, and the concrete on the top. As the bridge is loaded, the concrete compresses, and the steel pulls.
Pre-stressed concrete takes this one step further by putting the steel parts under tension before the concrete is poured.