The main point of being an anti-hero is about that moral ambiguity that comes along with all of their decisions/actions. For example the premise of House of Cards is Frank Underwood exacting his revenge on the people that went back on their word after he helped them gain power. Since you are seeing things from the anti-hero's perspective, you tend to sympathize with some of their aspects, while disliking some of the other things they do. Basically, these characters do things in a much more 'in your face' way that typically isn't seen with traditional hero protagonists.
The most interesting aspect of anti-heroes is that they turn tradition on its head and breathe life into stale tropes like the hero doing good, then saving the day. Of the characters that I named above, some consider themselves monsters (to an extent) (ex. Dexter), while others think of themselves as misunderstood or justified in their variety of actions (Walter White). Lately when you ask people about the best shows that have ever existed they mention things like The Sopranos, The Wire, Lost, Breaking Bad, and The Walking Dead , it's interesting to note that they all contain anti-heroes that walk the line between good and bad. Now you constantly see people saying things like "I am the one who knocks" and wearing the merchandise repping their favorite characters. This that this has become a phenomenon do to compelling writing that takes a character that could easily be turned into an evil character into a complex individual will many good, bad and ambivalent qualities.
I think that from here on out, only more of these morally grey characters will continue to exist and expand what we typically understand about what it means to be "good" or "bad". Their growing popularity will hopefully encourage studios to not play it safe and give us television shows that really challenge what we understand to be right or wrong.
