Gotham the TV show has worked so well because it presents the city of Gotham that we only get to see bits and pieces of in the Batman movies. We see the history of Detective Gordon, and Harvey Bullock, and the rise of power of some of Batman's greatest villains. We also get a back-story on Bruce Wayne as a kid growing up with no parents.
With the Batman movies, we got some insight into Detective Gordon but not much. We know from the Batman Begins, and the Dark Knight that hes married and has two kids. One of them turns out to be Batgirl. In Gotham, Gordon is new to the Gotham PD and is working with Detective Bullock.
Detective Harvey Bullock is a character that those that read the comic book now is Detective Gordon's partner originally. We don't know much about Harvey's past.
The Penguin is one of a lot of peoples favorite villains. He is a character with a bad temper, and willing to kill people just for staring at him the wrong way. In Gotham, we meet a young Oswald Cobblepot who is working for Fish Mooney, a new villain created just for the show. Cobblepot still wants to kill people, but apparently also wants to help the police catch criminals.
Catwoman is introduced as a girl around Bruce's age, who is orphaned and has cat like powers. She has taken a liking to Bruce and Detective Gordon, and is willing to help Detective Gordon catch criminals even at such a young age.
The Riddler is a crime technician working for the police department, always giving his answers in riddles. We don't get much of a story on the Riddler.
Bruce Wayne is a ten year old boy in the show, dealing with the death of his parents, and living with his butler Alfred. In the movies, we never got a story of what happened to Bruce between when his parents died, and when he donned the Batman mask. We got some background in the Dark Knight Trilogy, but this show goes into more of his background.
I think this show is what a lot of people who have watched all the Batman movies have wanted: the background on the city of [Gotham](series:1127075).