A tv-show about Captain America's boring girlfriend, taking place in the long dull time spawn between First Avenger and the modern movies? With Agent's of SHIELD I can sort of see the appeal since it takes place now, and will (to some extent) connect with the current events of the movies, but with Agent Carter I don't see the appeal. Unless you got tons and tons of free time and you need to absorb anything Marvel.
No offense to anyone watching the show, it might be great
Well, I think of it kind of like the comics (although I haven't read comics in YEARS now, but still). Let's say that at any given time, Marvel has 30 active titles. You might be actively into, let's say, 5 of those. But you like the characters in those a lot, and there are crossovers into issues with other characters, such that if you read the crossovers, you get a lot of really cool relevant background information and story about the 5 titles you are most into. So now you are into 10 titles, total--5 because you actively like them, and 5 because they fill in relevant information to the 5 you actively want to follow. It works similarly with the Marvel Movie/TV universe. Howard Stark and Peggy Carter are actually pretty important foundational characters for the present-day Marvel Universe. And Jarvis is pretty important as well. So I think it makes sense for a limited series focusing on those characters. It provides a more rich, developed backstory for a lot of related Marvel outlets, such as the films.
And as for Agents of SHIELD, while it functioned primarily as a spinoff of the films during season 1, season 2 made it an independent entity on equal footing with the films, IMO. It is now VERY connected with the films and is setting up a lot of what will happen in the films for the next few years.