In knitting, to cast on is to create the initial stitches that the work is built on. In effect, it's any process that creates a row of loops on the knitting needle that you can then knit the next row onto: the first instruction in a knitting pattern is generally "Cast on xx stitches".
There are a number of ways to do this. The simplest, and the one I most commonly use, starts with a slipknot around the "fixed" needle - that being the needle that usually holds the existing stitches, generally in the knitter's non-dominant hand. Knit one stitch from the slipknot, but instead of leaving it on the working needle, slip it onto the fixed needle. Create another stitch the same way, and another, and another, until you reach the number required by the pattern. This makes an edge that has a little - but not a lot - stretch to it. Other techniques will create a more flexible edge.