OHH!! This is short row knitting, and you're turning and wraping the yarn around a stitch. They call it TLPY (turn and loop yarn), but it's more commonly known as T&W (turn and wrap) or W&T (wrap and turn).
Knit the required number of stitches. Turn your work around just as if you had finished knitting the whole row.
Now, move the yarn to the back, and slip 1 stitch from the right needle to the left needle.
Move the yarn to the front between your needles.
Slip the stitch BACK to the right needle.
Now work the stitches back the way you just came.
You're simply taking your working yarn and wraping it around a stitch before continuing back the way you came. If you didn't do this, it would cause a hole in your work.
So.. you'll first knit 10 stitches, then turn & wrap the next stitch.
Then knit 5 stitches (these are 5 of the 10 you just knit), then turn & wrap again.
Hope this helps!