An original hem (also known as a Euro hem) is used when you desire to keep the distressed or faded look of the original hem. This is most often used on jeans. An original hem costs a little more than a new hem and also has a seam inside the jeans just above the hem.
Outside of Original Hem (Euro Hem)
Inside of Original Hem (Euro Hem)

A new hem is made by cutting off the original hem, folding up the fabric, and re-sewing the hem.

