When animal populations get isolated on islands, they often get smaller (as in big animals), or larger (as in small animals, like the wren). Big animals might get smaller because there is less space and food for them on the island, whereas small animals might get larger because there aren’t any other animals competing for food or predators waiting to eat them. There aren’t many immediate benefits to being larger; on the UK mainland the bigger birds would probably be able to out-compete other wrens and get most of the food and good resting places. On the island every wren is slightly larger, so that doesn’t happen. Larger animals do lose heat less rapidly, though, so the St. Kilda wrens may be a little better off when its cold.
I should point out that isolated animals don’t just suddenly become larger or smaller in their own lifetime. Size changes are adaptive and take several generations, at least.