The eyelet stitch is a way to make a "hole" in the finished knit, it comes in very handy for button holes and drawstrings. Here is how the stitch is done on a knitting loom, including the Knifty Knitter looms:
Step 1: Beginning at the position where you want the button, or drawstring hole, move the existing loop on the peg to the next peg on the loom.
Step 2: Bring the working yarn in front of the empty peg.
Step 3: Knit off on the peg that the loop was moved to treating both loops as if they are only one loop.
Step 4: When you have reached the next row, and reach the peg with the yarn stretched across it, treat it as you do any other loop on the peg while knitting off.
In addition to button holes and draw strings, some patterns call for this movement of the loops to the next peg in a repeated pattern to add new dimensions to the finished project.