Hi, welcome to the forum.
2nd row: 2nd row: Knit 1, * Purl1, Knit1B (b = knit into stitch bellow), rep from * to last two stitches, purl1, knit 1.
So you keep the edge stitches on each side in a regular plain stitch, then alternate purl and plain (knit) in the stitch below, on the middle part.
This row is kind of like a row of regular ribbing, but all of the plain stitches are done below (except for the edge stitches). You may never have ever done a plain (knit) into the stitch below before. It is one of those things in knitting that seem kind of weird, and maybe impossible, but is really easy. 
Because you did a plain row as row 1, you will have a purl row facing you as you begin this row. Instead of working a plain (knit) stitch into the stitch on the needle like you usually do, you insert the right needle into the hole that is right under the bump of the purl stitch that is right against the needle. Or you can think of it as right in the middle of the / that you see right under the purl stitch on the needle. You are actually knitting into the stitch in the row below instead of the one on the needle. You then yarn around like usual and pull the new loop up through the middle of that “below” stitch, then let the loop that is on the left needle come off.
It seems weird because you don’t ever really work the stitch on the needle, but you work into the stitch right under it and then let the one on the needle just come off. It seems like something might come undone or something, but it doesn’t. The result looks pretty much like a regular plain stitch but after you have a few inches of this done you will notice that it looks different.
Working in pattern as set (throughout) continue until hat measures 18 cm/7in ending with a wrong stitch row.
When it says this bit about “ending with a wrong stitch row”, I think they mean to end with a wrong side row. You didn’t say if they said whether row 1 or 2 was wrong side, but I did a couple of inches of this and both sides looks nice, but I think when you are working row 2 that you are working on the wrong side of the hat and that as you work row 1 the right side (side you will want to show) is facing you. So you end with a row 2 and begin the decreases on the row where all you do is plain across. That makes sense because the decreases will be easier to do on the plain row.
Just a note. I have not used knit in row below patterns very much. I have done the occasional K1B but on an overall pattern like this I have had trouble. If you make a mistake it is very hard to fix it. I wanted to make a little sweater that used K1B a lot and I had to give up on it because everytime I made the simpliest mistake I had to start the whole sweater over. 
I have a knitting friend who told me, “Don’t make any mistakes.” That sounded easy, but I couldn’t manage it. LOL I think I have the solution now. Use a lifeline regularly. Run a piece of waste yarn through the loops on the needle with a tapestry needle every once in a while (as close together as you don’t mind ripping out). When you are sure one section is perfect, you can leap frog the lifelines and reuse the bits of waste yarn.
I think this is going to be a neat hat, I’m not trying to discourage you in the least, but you might want to use the lifeline.
I have a knitting friend who told me, “Don’t make any mistakes.” That sounded easy, but I couldn’t manage it. LOL I think I have the solution now. Use a lifeline regularly. Run a piece of waste yarn through the loops on the needle with a tapestry needle every once in a while (as close together as you don’t mind ripping out). When you are sure one section is perfect, you can leap frog the lifelines and reuse the bits of waste yarn.