Arrow is based on the D.C. Comic superhero, the Green Arrow, who I really didn't know much about growing up. The show follows rich playboy, Oliver Queen, who returns home after being stranded on an island for five years. Before becoming stranded, he was on a boat with his father, his girlfriend's sister (who he was having an affair with) and some other people. The boat becomes shipwrecked and while on the emergency raft, his father gives him a list of corrupt individuals in the city to go after.
Queen returns home and takes on his new role as masked vigilante, Arrow, who obviously uses a bow-and-arrow as his weapon of choice. Why not a gun? I have no idea. I guess he may have been inspired by Daryl in the Walking Dead. While Queen plays a sarcastic, never-take-anything-too-seriously person in his daily life, he's all business when it comes to his inherited job and can beat up more people and dodge more bullets than Walker, Texas Ranger ever did.
The show reminds me of a manlier version of the series, Revenge. Hopefully it doesn't turn into a train wreck like that one did. And the best thing about is is that Mary actually tolerates it.