If you inquiring into arched-bridges, then you need to know how arches work in general.
An arch works because the stones lock each other into place, and direct the weight straight to ground. The better a curve you can get (less polygonish), the more efficient the weight distribution. Lintels and Columns (straight vertical and horizantal supports) are a lot less efficient in distributing weight, as they are basically square arches.
So how an arch bridge works is the way the stones (or metal beams) are placed. They are put so that weight is not focused on areas that are hard to brace. It works by making a sweeping curve with the material, and therefore directing the weight to strong foundations. It is a very effective tool first capitalized by the Romans.