Before medical science discovered how the circulatory system functioned, people believed that a vein of blood ran directly from the third finger on the left hand to the heart. Because of the hand-heart connection, they chose the descriptive name vena amori, Latin for the vein of love, for this particular vein. This theory has been since disproved, however the tradition remains in western cultures.
I was also believed that because the majority of the general population is right-handed, it was thought that the ring would be best preserved on the left hand, as it is not used as frequently as the right. As for the specific finger, the same reason applies. The ring finger is not used as much as the others because it’s said that this digit does not get as much use as say, the index or thumb.