Well for one thing, the story and characters are very well written. The TV series does have some inconsistencies, but overall, it's very well written. You get invested in these characters and it's not just about fighting zombies. It shows people getting crazy (in realistic ways) as the world falls apart and they fight to survive. To survive one must be strong mentally and physically.
Additionally, I would fit in in a post-apocalyptic world like that much better than this world. There's a town they get to at one point where everything is normal... they're hiding behind walls and the citizens of that town don't know what the world is actually like because they've been in this protected bubble. They think things are good but they're not. These people's houses are all clean, neat, tidy, spotless... they have a neighborhood where kids play and people walk their dogs and everyone there is smiling. Always smiling. They think this life they have is normal. They don't think it's so bad outside the walls just because they haven't
seen many zombies. They act like things such as not having unlimited hot water are big complaints.
One of the main characters, Carl, who is a kid at the time, says in the comic to his dad that the people are being stupid, because the zombies don't stop existing just because you can't see them. Other characters describe these people as seeming "fake" because none of them are aware of what reality is actually like and don't even care. Something very similar occurs in the TV series. All of this is important because that's how society is to me.
People with nice houses always smiling, acting like there's nothing wrong... whether they know any better or not, life's not so simple, it's not easy, it's not
like that. So I can't relate to these people. They're practically another species. I
scare them. Just like these characters in the series scared those townspeople. We look and sound wild and crazy to these people because they don't want the truth to be what it is.
If there weren't zombies in this series, I'd wanna live in a world like that... much fewer people, working in tight-knit groups to do things that matter, instead of stupid pointless crap like flippin' burgers or answering phones... actually knowing the people around you instead of just recognizing their faces... not having to worry about crap like money... that world isn't much worse than the one I live in, but their "society" actually makes sense whereas ours doesn’t.
Also, to quote what I wrote in another thread about characters I relate to:
From AMC's
The Walking Dead (note, not the comics, because I'm not very far in them and things tend to be different), the character I most relate to has been
Carl Grimes for a very long time. Reasons being that I'm good at surviving, as is he. I tend to be generally mature, but also naïve like a child/teen. I'm relatively knowledgeable about the way things are and am capable of making decisions on my own, but am more of a follower when given the choice and prefer to defer to someone else
whom I trust.... like my parents. I do possess some leadership qualities and am capable of taking care of myself; I am also very protective of those who have my loyalty, especially my little cousin (see: Judith). I do have some vague amount of hope for humanity even though people keep proving to be jerks again and again, but what matters most to me is my "pack;" my people. I also hate it when I can't be useful, which in fact may have been what first made me begin to relate to Carl, as early on he isn't allowed to help go on runs and fight the walkers (obviously, since he's a kid), but he understands (to a degree) the situation. He wants to help out, but he first has to prove to himself and to Rick that he is capable. He makes mistakes along the way and is forced to endure a lot of horrible things (such as having to shoot his own mother and being shot himself). He also gives people more chances than they deserve at times (
Ron 
) and I have been known to do that as well. I could probably go on and on about this, and this show in general, so I'll just leave it at that and can elaborate more if needed later on.
For clarification, I have read more of the comics since then and still definitely relate more to Carl than to like anyone ever.
Furthermore.... it's a zombie thing that's written well. I could go on about it forever.