The Muppet Show was a comedy-variety show that aired from 1976 to 1981, and the continued popularity of the Muppets, well into the 1980's, spawned a cartoon series and toy line based on that series. The cartoon ran from 1984 to 1991, and essentially featured the main Muppet gang as kids spending time together with their human nanny.
The original idea for a show about Muppet babies was spawned from the Muppets Take Manhattan movie, when Miss Piggy had a dream about what it would have been like to grow up with Kermit the Frog. The toy line consisted of things like plush dolls and action figures, and many of them ended up in Happy Meals at McDonalds. There were also bigger plush dolls and play sets, like the Muppet Babies Castle, in which to place action figures.