Hi and welcome to KH.
You're going to be working short rows to add width to part of the headband. I couldn't get a d/l of the pattern tonight, I'm not sure why, but will guess they're telling you to wrap and turn or to just turn. Here's the method I use, called German short rows
Basically, you knit part way across a row, turn your work, and continue knitting. When you're doing the short rows you'll be working flat even though the headband is knit in the round. Sometimes the only way for things like this to make sense is to actually see it done or better yet, do it yourself.