I understand how this fraud works. But how does the scammer profit
from it. Your phone bill is charge. Does the scammer get part of the charges?

I believe they are called "premium rate numbers". The only example I can think of offhand is where people call someone who talks "sexy" to them and the caller pays x dollars per minute. But they are used for other purposes too.
The billing is routed thru the phone company and the sponsor of the line gets a check from the phone company and pays a fee for the premium rate service. The person/company who sets up the premium service let's say pays 5 dollars per call to have the service and the perp (In the case of scams) charges let's say 10 dollars per minute. So he keeps you on the line for ten minutes, he nets (10x10 minus the 5 charge he incurs) $ 95 on that one call.
I am guessing at the rates but that gives you an idea of how the perp makes his dough, but there are many legitimate uses of the system too.
Maybe an ace mechanic could set one up and folks would call the mechanic and he would charge them per minute of discussion on how to fix the problem with their car.
Premium-rate telephone number - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Premium-rate_telephone_number)

I believe they are called "premium rate numbers". The only example I can think of offhand is where people call someone who talks "sexy" to them and the caller pays x dollars per minute. But they are used for other purposes too.
The billing is routed thru the phone company and the sponsor of the line gets a check from the phone company and pays a fee for the premium rate service. The person/company who sets up the premium service let's say pays 5 dollars per call to have the service and the perp (In the case of scams) charges let's say 10 dollars per minute. So he keeps you on the line for ten minutes, he nets (10x10 minus the 5 charge he incurs) $ 95 on that one call.
I am guessing at the rates but that gives you an idea of how the perp makes his dough, but there are many legitimate uses of the system too.
Maybe an ace mechanic could set one up and folks would call the mechanic and he would charge them per minute of discussion on how to fix the problem with their car.
Premium-rate telephone number - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Premium-rate_telephone_number)

I get it. This exchange comes from the Caribbean islands Dominican Republic
You receive a anonymous call not giving any information, hoping your curious enough to call them back.Viola your done.

Yes, the fact that you initiate the call puts you in a very bad position when the phone bill arrives with possibly a several thousand dollar charge listed, and you can't get it cancelled, so some reports have indicated.
But, the emails that spread this story around said -Don't ever call an 809 area code-- and the fact check organizations say that there are legitimate 809 area code numbers.
Best practice is- never call a phone number unless you know something about that number.
I don't even let unknown 800 type numbers go onto my answering machine (at least not when I am home). I hit the speaker button to pick up the call and immediately hit off.
They rarely call back. I think that with computer generated calls, that split second of connection (picking up and quickly hanging up) tell the computer that the call was answered and their "deal" was rejected. If the call goes onto the answering machine, it may be programmed to try that number again. But that's just my theory.