This pattern is called “Mirror Braid.” The knits and purls to each side of the pattern are for knitting in the round, for the gloves I make, and can be ignored if you are using this pattern for a hat or scarf.
This pattern, and in fact most of my patterns, revolves around cable knitting. A quick explanation for cable knitting can be found here at Knitting Help. The key has a couple of abbreviations that you might have never seen.
The first abbreviation is CB and it means cable back. To cable back you take the first half of the stitches marked to be cabled on the chart and place them on the cable needle, or dpn. Then you place the cable needle in the back of the work and knit the other half of the marked stitches. In this chart there are 6 stitches for every cable, so you would place 3 stitches on the cable needle, place them in the back of the work, and then knit the next three stitches. After this you will knit the three stitches from the cable needle and then continue the piece. The way this is generally seen on knitting chart keys is C6B, but as I use graph paper I use each square as a stitch so the number I am cabling is evident to me (and sometimes can change over the course of a pattern).
The second abbreviation is CF which means cable forward. You will repeat the process that is seen above, except for the placement of the cable needle. Instead of putting the cable needle in the back of the work you will place it in the front of the work and then follow the rest of the instructions for cabling. Here is the picture of the finished project.