Can't understand pattern

Making a hat…
First part of the hat is finished…
I believe now I must start decreasing to shape the hat…
This is what the pattern says…

Shape top: 1st row: (RS). K1. *K2tog. K10 (5-10). Rep from * to last st. K1. 68 (74-79) sts rem.
2nd and alt rows: Purl.
3rd row: K1. *K2tog. K9 (10-9). Rep from * to last st. K1. 62 (68-72) sts rem.
5th row: K1. *K2tog. K8 (9-8). Rep from * to last st. K1. 56 (62-65) sts rem.
7th row: K1. *K2tog. K7 (8-7). Rep from * to last st. K1. 50 (56-58) sts rem.
9th row: K1. *K2tog. K6 (7-6). Rep from * to last st. K1. 44 (50-51) sts rem.
11th row: K1. *K2tog. K5 (4-5). Rep from * to last st. K1. 38 (42-44) sts rem.
13th row: K1. *K2tog. Rep from * to last st. K1. 20 (22-23) sts rem. Break yarn, leaving a long end. Draw end tightly through rem sts and fasten securely. Sew back seam.

The problem I am having is when I leave the stitches do I leave them on the left needle and wrap around and go back or slip them to the right…
After that on the alt rows do I purl the stitches or ignore them…

Help Please!!!

Hi and welcome!
In each of the rows, you should knit to the end of the row, decreasing at the given intervals (k2tog, k10 or k2tog k9 or k2tog k8 etc). At the last stitch, k1. When you get to the end of the row, there won’t be any more sts on the left needle. Just turn as usual at the end of a row and purl all the stitches until you get to the end of that row too.

I don’t get it…
What’s the point of putting stitches remaining then…

If you count your stitches at the end of the row, you know if you got it right. The number of stitches remaining is the number of stitches on the right (which will now become the left) needle. It’s an opportunity to check for mistakes.

I see!!
Thank You!!!