I'm an Avon lady, although I don't do it for the money - which is a good thing as I only have a few customers. I only do it because I like the products and didn't know a rep. I just do it as a favour for family and friends, basically.
Anyway, how it works:
There's a campaign (catalogue) every three weeks. Your customers order the stuff from you, which you then order from Avon. You deliver the goods to your customers, they pay you, and you pay the money to Avon. Avon likes you to take payments in cash (they won't accept third party cheques) and then either pay them online, by cheque or in cash at a Post Office. Some reps, it their sales warrant it, open business bank accounts so that they can take customer cheques themselves and then pay Avon out of the account, although it's not something Avon recommends.
Ordinarily you don't make a profit during a campaign unless your sales are above a certain amount (I think it's around the £70 mark). Sometimes Avon has special promotions where you can make a set profit on certain items. Your profit is what's left when you've collected the money and paid the invoice. There's also 'Presidents Club' where, once you've made a certain sales target for the year, you get extra offers and discounts and invites to special events.
You do have to buy the books, samples, sales aids and demonstration (new) products. You get the demo products at a decent discount and I often end up buying them just because I like them. They sometimes make nice presents for people too, which is a good way of getting more orders.
In short, profits aren't huge, and you do have to work very hard to make anything substantial, but plenty of people do it successfully and thoroughly enjoy it. It's easier if you're a natural sales person, which I'm not, but then I don't especially want to be.