Garter stitch is knit every row, but you are supposed to do all the knitting through the back loop. As a stitch sits on the left needle waiting to be knit it has a leg on the near side of the needle and one on the far side of the needle. You are going to knit into the back leg instead of the front one like normal. It's actually more like the way you insert the needle for a normal purl stitch, but instead of inserting the needle into the front leg of the stitch like you do to purl, insert the needle, as if to purl, but behind the needle, in the back leg.
I've never seen twisted purl done, but that is what it is telling you to do. I hope that helps.