A swatch is just casting on a bunch of stitches 20-30, and knitting a couple inches. Call it a sample
It can be used to tell you how many sts per inch (or 4"), what the stitch pattern looks like, and how the yarn looks when knit. Not all sweaters, whether for dogs or people, are knit in pieces and seamed, there's many that are seamless. For the leg holes, you'd knit the body in the round, BO some sts for the openings, knit flat on 2 or 3 sections for a while, then cast on some sts to join it all in one piece again to finish up. No seams, or very minimal at least.