What the heck is Baker's Sugar?

So reading through the Cake Bible, I found out that most commercial bakeries use something called "Baker's Sugar". It's apparently more fine than granulated, and will make a lighter, fluffier cake.
I did notice that the granulated sugar crystals in the United States are larger than the ones I was used to in Japan. I wasn't sure if it really made much of a difference, but the other day I noticed a box of "Baker's Sugar" at the supermarket that was reasonably priced so I thought, why not?

The crystals on the left are regular, granulated sugar. On the right is Baker's Sugar. It has a consistency like NutraSweet or whatever those artificial sweeteners are called. When I creamed it with my butter I definitely noticed a difference. The butter mixture looked a lot smoother and it blended faster than usual. As for the final product, I have never found my cakes to be grainy, so I couldn't really tell the difference. I'll keep using the Baker's Sugar I bought until I run out, but I'm not sure if it's necessary to go for the finer grain, unless I'm making something super light like chiffon cake. Maybe once I understand cake baking a little better I'll have a better idea of whether I should continue using Baker's Sugar instead of granulated. Or I could just buy a food processor like I have been wanting to and make a finer grain myself....