A peach sapphire ring is any ring that contains a peach sapphire. True peach sapphires, or padparascha sapphires, are very rare, but methods exist for artificially infusing a sapphire with peach color.
Sapphires are a formation of corundum that can come in a variety of colors based on the trace amounts of other elements found in the crystal formation. Blue is the most common color found. Peach sapphires are among the rarest, fetching anywhere from $1,000 or more per carat, depending on hue and purity.
Sapphires can be treated to have a peach color. This process involves heating the sapphire almost to the melting point, then diffusing impurities into it. Artificial peach sapphires are less expensive, but they are also hard to detect. Treated sapphires are required by law to come with documentation.