I've been making amigurumi for a while, but I've only recently started turning them inside-out; I think it's mostly a matter of choice. What do I mean when I say turning them inside-out? Here you go!
When you crochet in the round (as you do when you are making amigurumi parts), there is a significant difference between the way the stitches look on the outside, and the inside. I usually leave it as-is and stuff and sew the pieces together. However, I think many people like to turn those pieces inside-out; it makes a difference in appearance! On the outside, the stitches are more rectangular, but when turned inside-out, they appear rounder and fuller. In terms of aesthetics, turning them inside out means that your amigurumi's stuffing is less visible, such that the very same amount of stuffing in an item will show LESS in an item that is turned inside-out than in an item that is just stuffed right after you finish crocheting.