Harajuku Bridge is famous because it has long been a weekend hangout spot for the Japanese girls (and a few guys) who are involved in Harajuku's unique fashion scene. The term "Harajuku Girls" was coined about the girls who gather on the bridge. The fashion styles on the bridge vary widely, but the two most popular groups are either some type of lolita fashion or people doing cosplay. The cosplay on the bridge varies, but is often based around popular Japanese visual kei bands.
Before 1996, when the Harajuku Hokoten was still active, the bridge was a lot more crowded with cosplayers, gothic lolitas, and other strange fashion styles. While the popularity of the bridge as a hangout has died down somewhat in the 2000's, there are still girls that hang out there each weekend. Sunday is the day when the most Japanese kids hang out on the bridge.
The bridge is also a very popular weekend destination for tourists who visit Japan. On some weekends, you will see far more tourists taking pictures of Harajuku Girls than you will see actual Harajuku Girls.