This is similar to k1, yo, k1 into one stitch if you've ever done that. In this pattern, you'll keep repeating the ki,yo,k1 until you have 7 sts on the needle. (The video shows 5sts in one so just do one more yo, k1.) The difference with the Waterlily pattern is that instead of working into a plain knit st, you're working into a k3tog.
So k3tog but before you drop the st from the needle, go back into it and k1,yo,k1 etc until you have 7sts on the right needle and then drop the st from the left needle. It makes the candleflame or waterlily at the center of the diamond pattern in the shawl.