This is way outside of the scope of what can be answered in a blog post but I'll take a quick try
Wisedave's post is a huge part of it - the cash back company get a commission from every customer they send. They credit back a portion of this (sometimes even 100% or more, I'll get to that point) and anything left over is profit.
An absolutely massive part of the business model is dormant accounts. They will all have minimum payouts before a user gets any cash back. A huge amount of people will sign up and make 1 or 2 transactions, never hit the cash out limit and never use the site again. This means these accounts have been credited but will never be paid out - the cash back company keep this money.
Then you have a nice revenue stream from non signed up users. Lets say for example they have a page offering cash back of £10 if you sign up for Sky tv (complete random example). Sky TV pay the cash back company £10 for every signed up customer. The cash back company pay their users £10... so it looks like they can't make any money. But you've got the people above who never actually cash out of course. Then you've got a lot of people who find this page and click through because its a good deal... but they aren't a member. So there is no account to be credited back to - the cash back company pocket this commission.
Then you have outright fraud. People sign up and defraud companies all over the place, getting payouts in the thousands. Any that are caught are obviously deleted from the system. But its rare for the companies to claw back the money from the cash back company. So if a fraudster signs up and has several months of making £500 each time on fraudulent transactions, then gets caught and cancelled in month 6 with £450 pending... the cash back company keeps the £450. Bear in mind they haven't actually lost anything in the first 5 months as merchants paid out. So this customer is positive £450 on the bottom line.
Then you have onsite advertising. A lot of these sites get a huge amount of traffic. Many of them will run Adsense (the other end of Google Adwords) getting paid per click. Or they will sell ads direct etc.
Then you have overrides and kickbacks from affiliate networks. Another made up example just to show how this works. Lets say Currys offer 10% off laptops with a discount code. This is handled by an affiliate network who get a couple of % on top of this. Cashback site then agrees to pass on the full 10%, so apparently making nothing again. (bear in mind they take several bites of the cake from the methods outlined above anyway). Affiliate network love customers who can push huge volume like this... they kick back a chunk of their commission straight to the owner of the cash back site.
Then you have cookie stuffing. Probably too tech for most of the readers here so I'll save that one
Then you have seo pages... cash back sites build up a lot of strength in Googles eyes. So the owner creates a bunch of pages on them to rank for specific high value phrases. These generate a lot of sales and income in their own right, and again they take further slices of the income from everything above again.
I could write thousands of words on this but I'll stop now before I bore everyone.
