If you're looking to make something extremely warm and cozy while also learning a new technique, brioche stitch is a great choice. The stitch is made by working yarn overs and slipped stitches, and knitting (or purling) them together to create what looks like an extremely puffy one-by-one rib. Confused? That's OK, it makes more sense when you try it.
Brioche is a little complicated and confusing when you first set out to try it, but starts to make more sense when you get into it. If you try to read a brioche pattern without working it, your eyes will probably glaze over and cross, but I promise -- it's not so bad once you learn the terminology and get a feel for the stitches. In fact, it's addictive -- you'll be cranking out lofty, toasty pieces in one color and two color brioche, worked flat and in the round, and so on.
You have to start with a set-up row, and you have to know what the terms are. Yes, it has its own terms -- and its own website, which is where the following terms came from:
BRK -- brioche knit, or "bark" -- knit the slipped stitch from the previous row together with the YO next to it
BRP -- brioche purl, or "burp" -- purl the slipped stitch from the previous row together with the YO next to it
sl1yo -- this is where the brioche stitch gets its puff, and it's done differently depending on whether you're working a "bark" or "burp" row. When it follows a knit or BRK stitch, it goes as follows: bring the yarn UNDER the needle to the front, slip the next stitch, then move the yarn OVER the needle to the back. When it follows a purl or BRP, you slip the stitch THEN move the yarn over the needle to the back, around the slipped stitch, and back to the front.
If you're working a flat piece, you only need two rows: the set-up row and the BRK row. To do that, you'll cast on an even number of stitches. Then work the set-up row as follows: *sl1yo, k1* across. Every row after that will be: *sl1yo, BRK* across.
You'll need the BRP row if you decide to work brioche in the round (which you should -- a brioche cowl is just about the most luxurious thing to wear when it's bitterly cold out). You'll cast on an even number of stitches again, and, working in the round, do the same set-up row: *sl1yo, k1* around. Then you will alternate between two rows. Row 1 is * sl1yo, brk1* around. Row 2 is *brp1, sl1yo* around.
You can also work brioche with two colors, which gives a garment a beautiful depth. You can read about that here, but wait until you've got the hang of single color first. As you can see below in the Triple Ruff pattern, two-color brioche looks fantastic and rich.
Don't be scared to try brioche stitch! It looks complicated, but you'll get the hang of it really fast, and then you'll have a pretty new technique in your repertoire. The best way to learn it is to just do it. Work the stitches as you read about them, so you can see and feel what they are.