What if you were a genius, and your father was a deadbeat who abandoned your family and treated you miserably? You might then grow up to be one of the Tenenbaums. A bunch of seriously surreal neurotic messes. It's even worse for the one who's adopted. Each of the Tenenbaum children - adults for most of the movie - has their own particular brand of idiosyncracies and "issues."
When their father, Royal, comes back on the scene after decades, it all comes to a head. Although Royal wants to "reconnect with" (read "use") his family, they're ambivalent about his return. Each reacts according to their own quirks, and this mismatched family bands together both for and against the unwelcome father.
The film has its high and low points, but taken all together, it's a decent story.