The white wedding dress is actually quite a recent tradition - not nearly as ancient as it seems. Before the nineteenth century, brides got married in dresses of all different colors, often in dark or bright shades. White was expensive and impractical; it was hard to keep clean. The turning point came when Queen Victoria got married in a white dress - it became a symbol of purity and innocence, and the fashion quickly spread throughout Europe and beyond. After that, white became firmly established in Western tradition as almost mandatory.
Nowadays, the white dress remains popular in many countries because the tradition has taken deep root and is passed down from generation to generation. Plus there's a practical side to it: white is versatile, looks beautiful in photos, and dressmakers have been trained to sew these dresses, so there's a huge selection. But mainly it's just become a social expectation, and people follow it without even thinking about where it came from.
Though honestly, more and more brides are choosing what they actually like now. Some wear a colored dress, some beige or silver. If you like white - great, if not - it's not required. Modern weddings are increasingly becoming an expression of personality rather than following a rigid set of rules.