A great source for a lot of information on this intrepid pair can be seen at Nero Wolfe's Wikipedia Entry.
The short form:
Born in the Balkan state of Montenegro, Nero Wolfe is a genius, an eccentric, an agoraphobe, and probably the greatest private detective in the world.
He lives in a brownstone house at 922 East 35th Street, in New York City, with his able assistant, Archie Goodwin, and his chef and housekeeper, Fritz Brenner. He is a very fat man (at least the whippet-thin Rex Stout, who created him, thought so, referring frequently to his seventh of a ton. That's only 285 pounds, but Stout, who was probably about 160 pounds soaking wet, probably thought that prodigious.) a gourmand, chef, and orchid grower who never leaves his house on business, and keeps rigidly to a schedule: From nine to eleven each morning, and from four to six each afternoon, he ascends in his private elevator to the greenhouse on the roof of his three-story residence to work with his orchids, assisted by a daytime employee named Theodore Horstmann, who is seldom seen. Wolfe will not discuss business at meals, drinks far too much beer and is quite fussy about language, sometimes charging clients higher fees -- and his fees are prodigious -- if they dare to use "Contact" as a verb.
His stories are narrated by Archie Goodwin. Goodwin is a first-class private eye, tall, strong, handsome, brave, with a photographic memory. He has a thousand jobs with Wolfe, but the two main ones are these: He does all the actual "Investigating" when Wolfe is hired to solve a mystery. He visits crime scenes, questions witnesses, gathers evidence, takes notes, memorizes conversations. Then, later, back at the office, he tells Wolfe all that he learned, often verbatim. Wolfe then solves the case. His second job is to ride Wolfe and make sure he actually works. Wolfe is a deeply lazy man, and would end up penniless and homeless without Archie Goodwin to hector and annoy him into doing his job. Goodwin is likeable and sarcastic, and forgets nothing. Archie will do a fairly good job of introducing you to other characters, so trust him to guide you: Wolfe won't always play fair with him, but he will always play fair with you.
Most of you know "Doctor Who" at least from the new series, so you'll know the Tenth Doctor and Martha Jones. Later, we'll be spending time with the Third Doctor and Jo Grant, who few of you will know, but I hope you'll give them a chance.
To the best of my ability, though, this story will be told in the fashion of a Nero Wolfe mystery story, so please be prepared for that point of view.
One more point about the Wolfe characters: They don't age. It was a deliberate choice by the author: From 1934's "Fer de Lance" to 1975's "A Family Affair," published just a month before the death of Stout, Wolfe has remained in his fifties and Archie in his early 30s, while world events stay current and pointed. This is at times very "In your face:" In 1964's "A Right to Die," 50-ish Wolfe and 30-ish Archie are hired by character from 1936's "Too Many Cooks," who explicitly states that they first and last met him 28 years before. That's just the fact of the Wolfe universe, and one I'm adhering to, with an opening chapter set in 1968 before the story picks up in "The Present Day."
So I hope you'll come along with me and meet Wolfe and Archie. If you like them -- and I believe you will, or I wouldn't be here -- pick up Stout's original books: they're still easy to find. I also recomend the recent A&E TV Series "A Nero Wolfe Adventure" starring Maury Chaykin as Wolfe and Timothy Hutton as Archie, seen in my Icon.