Stamp seals first appeared in Mesopotamia around the early 6th millennium BC. They were used as an administrative tool, acting as a signature, for stamping on clay surfaces, as were the cylinder seals invented in the 4th millennium BC. Traditional Mesopotamian seals had a profound aesthetic influence on the peripheral regions, among which Anatolian stamp seals inherited most of the typical features from the Old Assyrian period (circa 2000-1700 BC).
For more about stamp seals, see our relevant blog post: Making their Mark