The show is said to be "Eddie Munster's story," the werewolf son of Herman and Lily Munster. The opening sequence is from a summer camp, where several boys and girls are attacked by Eddie while in his werewolf form, which forces the family to move into the shoddy mansion in Mockingbird Heights. Here's a description of Eddie's character.
"Think Rick Schroder in The Champ - with sharper teeth. The first - and he's seemingly the most central character - of The Munsters we're introduced to. Much like Michael J. Fox's character in Teen Wolf he's about to discover he's got quite the howl- - only he's terrified beyond belief at what that means (he's frightened enough of puberty!). Though The Munsters have moved to Mockingbird Heights because Eddie attacked his fellow boy scouts at a camp, he doesn't have any recollection of the event and has been told a baby bear attacked his friends. Eventually Herman is forced to tell Eddie what he does, as the request of Grandpa but dad's determined to remind him - just as his mother will - that he's not a monster. Young Eddie ultimately decides to be a vegetarian monster when he can help it, and when he can't... his dad says they'll figure it out together. Awww."
to read more about The Munsters, including breakdowns on the rest of the characters, and more plot details, with spoilers.