According to Mary Brooks Picken’s The Language of Fashion (1939), sheath dresses first emerged as full length gowns around 1910. They were “straight, narrow, and close fitting, with a tube-like silhouette.” In a knee length version, they came back into fashion in the 1960s, made famous in the US by Jacqueline Kennedy. It is worth noting that Michelle Obama has also made this look her own.
If my photo collection is at all representative, many older women chose sheath dresses in the 1960s. They were simple, stylish, and could be made to flatter older shapes (although they didn’t always).
These two women have very similar styles, judging by their hairdos, glasses, shoes, and necklaces. They both wear very colorful sheaths. In this photo, the one on the left had better luck making the dress work for her. Perhaps it is the longer length and roomier shape.