Well, to modern eyes those dress uniforms are a bit garish. However, the Swiss Guard is an elite military force, trained in all sorts of weaponry and such. It wouldn't pay to mess with one of them, even if he was wearing the funny uniform.
For some history of the Swiss Guard see:http://www.vatican.va/roman_curia/swiss_guard/swissguard/storia_en.htm
What you see are the uniforms designed by Michaelangelo IIRC.
In an era when there were no standing armies, much less well trained ones, they were the best. Available at high cost. As one king said, "No money, no Swiss"