It's a compilation tape that was released in 1985.
The Kermit and Piggy Story shows... well, Kermit and Piggy at dinner in a fancy restaurant remembering the good times, and the not so good times from The Muppet Show. From Miss Piggy's very first appearance as an obsessed chorus girl singing "Temptation", to Kermit and Piggy's "wedding", to Kermit singing "Ukulele Lady" to Piggy. Even this old favorite:
The frog has come to have his say,
The pig'll never get her way.
Bib and napkin, knife and fork
Is the only way that I'll touch pork.
The show ends with Kermit looking over Miss Piggy's bill...
PIGGY: I think I'll go get a pizza.
KERMIT: I think I'll stay here and wash the dishes.