The buyer discloses the financing arrangements to the seller because it makes his offer more attractive.
When a seller receives and accepts an offer, the deal does not usually close until 30 to 60 days later. If the buyer cannot come up with the money by closing, the deal falls apart. This is a risk for the seller.
When a seller is considering whether or not to accept an offer, it is helpful to know the likelihood that the buyer can actually obtain the amount of cash in the offer by the closing date. If the buyer can't acquire the funding, the offer isn't worth the paper it is printed on.
The amount of the down payment vs. the amount of financing is also relevant to the seller. Let me give you a real-world example that happened to me once when I was selling a house. The buyer was doing a no-money-down mortgage and had no money for a down payment. He was even borrowing the closing costs. We accepted the offer, but when the bank did the appraisal, it was short of the purchase price. For most home sales, this would not be a problem, as long as the appraisal was more than the amount borrowed. But in this case, because the amount borrowed was more than the appraisal, the bank had a problem. The deal was at risk, and in order to continue either the buyer had to find some money somewhere (which he couldn't), or we had to lower the price to save the deal. Certainly, accepting the offer from a buyer with no cash to bring to the table was a risk.
(In our case, we got lucky. We found some errors that were made in the appraisal, and got it redone.)