A local game shop is a shop where you can go and purchase games, typically board games, card games (tcg, or trading card games, lcg, or living card games), miniature games, role-playing games (Dungeons & Dragons, Pathfinder, Werewolf the Apocalypse, Vampire the Masquerade, and many many others) in which you assume the role of a character you create and roll dice to help randomize the successes and failures of your character. To go with the RPGs and miniature games I also sell dice.
Magic the Gathering is the first, largest, and oldest of the Trading Card Games (TCGs) where you buy packs of randomized cards and use those cards to build a deck to compete against other players. Other games in the genre as Pokémon TCG, YuGiOh!, Lorcana, Flesh and Blood, Weiß Schwarz, and Star Wars Unlimited.
You might check out the tcg then.