.. a ring made in two parts, “male” and “female”. A hole is punched through all layers of fabric. The female part is on one side, and the male part goes through the fabric. Since the male part is slightly flared, a grommet machine or tool is like a pair of specialized pliers. It “crimps” the male and female together, folding the male part into the female.
(Modern day brass and aluminum grommets are not strong – but they don’t rust either!)