The edges of woven fabrics will fray unless they are finished or covered by a lining. Fraying is the ravelling of fabric edges that occurs. Some fabrics will fray more than others.
Some of the most common methods you can use to finish the edge of your fabrics to prevent this fraying include: trimming with pinking shears, overlocking, binding, constructing French seams and overcasting.
Overcasting is very accessible, because you can do it with your sewing machine. A simple overcasting method is to zig zag the edges of your fabrics. A smaller zig zag is selected for lightweight fabrics and a larger zig zag for heavyweight, bulky fabrics.

Your sewing machine may also have an overcasting stitch which will simultaneously create a seam and overcast the edges of the fabric. Additionally, your machine may have come with an overcasting foot which allows for the perfect placement of your fabric and leaves the stitch neatly laying on the edge of the fabric.
