Sewing: The side of the fabric or garment that will show on the outside.
Most fabric is sold folded over lengthwise, right sides together. You don't have to go with the manufacturer's designation, though. Some fabrics (like denim) have one side that is conventionally considered the "right side". Others look the same on both sides, and are entirely reversible. If there is a difference, and there is no convention, you can pick which side you prefer to be "right".
In addition, seams are generally sewn right side to right side, so that the ragged edges are on the inside of the finished product.
In pattern notation, the right side is generally shaded.