All they tell you is someone played arena enough times to get one. Undead Match can be fun, but these badges are meaningless.

Of course, any losses in the time in which you are attempting to rank up will increase the total number of matches needed to rank up. If you are demoted, you can still regain your previous rank by winning the required number of matches to ascertain the next rank. There are four honor ranks: Iron, Bronze, Silver and Gold. Consecutive losses will lead to a rank demotion. The exact arena rank system is currently uncertain. The Badges will be showed beside the name of the phantom when summoned into another world (Even for co-op or invasions) and can be checked in the right corner of the Undead Match menu in the Firelink Shrine Bonfire after acquiring and burning the Champion's Bones. There are 2 different badges, Duel Honor for the 1v1 duels and Brawl/Co-op Match Honor for the Brawls and Co-op matches. The Badges will change depending on the honor or rank achieved in the arena. Badges in Dark Souls 3 are icons earned from competing in the Hollow Arena.

Dark souls 3 duel arena