Daniel. In order to use unslotted bridge pins the bridge has to be slotted which involves cutting a slot along the side of each bridge pin hole (on the saddle side of the hole) for the strings to fit into so that they don't take up any space in the hole itself. When that's done a solid/slotless pin can fit into the hole which serves the purpose of holding the ball end of the string against the under surface of the bridge. When the bridge pin holes are not slotted, you need to have the slots for the string to fit into, in the bridge pins themselves. When this is the arrangement, the ball end of the string rides up into the pin and the hole, distorting the shape of the pin and eroding away the lining of the hole.
With solid pins and slotted bridge pin holes the ball end of the string rests on a flat surface. That gives it more solid contact with the soundboard and transmits the sound better than when it's trying to pull through the gap between the slotted bridge pin and the inside edge of the pin hole. As a result the tone (at least I think so after doing this on several guitars) is improved. In my experience sustain, clarity, and volume are often noticeably increased.
This says it better:
http://www.bryankimsey.com/bridges/slotted.htm