Not only do white fillings blend in better with the rest of your teeth, but they also help the tooth around the filling to remain strong. Over time, amalgam fillings create stress on your tooth and lead to your tooth cracking or letting decay leak down underneath; white fillings, however, do not cause as much stress on the tooth.
They also help to insulate the tooth against wide temperature changes.
If the cavity is large, a porcelain overlay or cap may be put on top of the white filling in order to provide additional support and strength to the tooth. They work extremely well on their own in small cavities though.