A Mirror Match is a Duel played between two people whose Decks are nearly identical, use cards from the same archetypes, or focus on roughly the same strategy.
A first example would be two Duelists using an identical/nearly identical Deck, like when (in the anime) Yugi and Yami Yugi dueled in Episode 163 (where the only card that made a difference between both Duelists' Decks was "The Seal of Orichalcos"). In Yu-Gi-Oh! Duelists of the Roses and Yu-Gi-Oh! Forbidden Memories, Deck Master K uses a Deck identical to yours as well.
A second example would be two Duelists focusing on the same concept while using different cards, such as both players using the "Exodia" cards while using different draw engines, or both focusing on burn effects while using different burn engines.
A third example would be using cards from the same archetype differently, such as one player using the material-specific "Elemental HERO" Fusions ("Shining Flare"/"Flame Wingman", "Rampart Blaster", "Thunder Giant", etc.) and one player using the "Omni HERO" (unofficial term) Fusions ("Absolute Zero", "Nova Master", 'The Shining", etc.), in which case both would have relatively the same Main Decks but different Extra Decks.