Each Final Fantasy story is different, though there are reoccurring names, plot points, and themes. Generally, each game is about a group of warriors or adventurers that end up facing a world-devastating or world-destroying threat and their quest to stop it, usually gaining a power given to them by magical crystals.
Each game has different vibes, however. For instance, Final Fantasy IV is about a corrupt royal kingdom and the people that serve within it discovering what they are doing and turning on the corruption; Final Fantasy VII is about a group of rebels fighting against a worldwide company that creates a fuel source that is slowly killing the planet; Final Fantasy XII about spirits manipulating mankind to do their bidding. Each game's theme is often also demonstrated in the title image of the game: V has a dragon, as Reina, one of the characters has an affinity with dragons; VIII has the two main protagonists Squall and Rinoa embracing, as romance is the central through-line of the story; IX was the crystal, as kuja, the main antagonist figures out that he can not live forever, he sought to destroy the crystal of life, destroying all life with him; X has heroine Yuna doing a ritualistic dance for the dead, as death is a central theme.