You are actually twisting the whole work around and not just a stitch. On the hat you knit a garter border and then on the twist row when it tells you to, you rotate the left needle tip toward your body then keep rotating it all the way around until it has gone in a full circle and is back in the normal position and then knit the next st to keep it put. Continue across the row rotating the left needle when they tell you to. This literally twists the edge all up. On the hat you only do it on this one row and then you switch to dpns and join and work the hat normally.
I looked at the sweater. On it I think it said to twist the border and then you do the twist also on the neck trim. You cast on the stitches for it, do some garter then twist it and then to attach it to the sweater neck you use a 3 needle bind off.
If you don't want to do the twists they wouldn't be necessary. They are a little weird looking to me, but if you want them they are not that hard. The rest of the sweater and hat is normal and you don't do the twist all over the place.