Every machine has at least a couple of overcast stitches. The zig zag stitch is one but your machine may have more. Here is a picture of the overcast stitches on my machine (look at numbers 10 - 14):
The letters under the stitch tell you which presser foot to use (there is a letter imprinted on each foot on the inside). I often use stitch number 12 with my overcast foot to finish off the edges of my seams. You can also use the zig zag stitch and this foot (even though you can use the "normal" sewing foot as well).
You want to finish off the edges of your fabric to keep them from fraying after being washed and used and there are several different ways of doing this. Hemming, pinking shears, overcast stitches....are all ways to finish off edges.
Here are some pictures of a pillowcase I was working on and how I finished off the seams on the inside. I first sewed my seam of a 1/2" seam allowance and then I used my overcast foot and finished off the edges of the seam:
I used the regular zig zag stitch on the seam above. In the first picture, you can see how the fabric is put underneath the presser foot. There is a piece on the foot that you guide the fabric along up next to. That way, when the needle swings over to the right, it goes right off the edge of the fabric encasing it. I often do this projects that I know will be laundered quite frequently such as children's clothing and pillowcases.