It sounds like the stiches you are referring to is what is known as free motion quilting (FMQ). This stitching is done towards the end of the quilt-making process, once the top, batting, and backing have been layered together. There are specialized machines, called long-arm machines, that make it easier to do this. It can also be done with certain types of regualr machines, but can be more difficult do to having less room to manuever the quilt.
As for how the stitches look so great, practice! Some of the fancier machines also have some computer guidance. I haven't attempted FMQ yet myself, but I have read a lot about it. It can also be done by hand, of course, but that will take much longer!
I hope this was what you were referring to, and that this wasn't a rehash of things you already know! There is a lot to learn with quilting, but once you have some of the basics down, it's much easier to learn new concepts.