The brk (brioche knit) stitch is always worked together in combination with a slyo (slip and yarn over), and they combine with the brp (brioche purl) stitch, to create the typical brioche fabric together.
Brk: On the knit column, knit the next stitch together with its corresponding yarn over. When you are working the purl columns in a contrast colour like in the video, the yarn over will be the contrast colour, and the stitch the main colour.
Slyo: Bring the yarn forward in between the two needles. Slip the next stitch (which is a purl stitch) from left to right needle as if you are purling it, and keep the working yarn at the back to work the next knit stitch. You have now added a yarn over in the main colour to the purl stitch in the main colour.