What does freely assignable and the contract is silent mean in real estate? Do these benefit the buyer or seller?

The two phrases in your question "freely assignable" and "contract is silent" could apply to a few things separately, but when taken together it seems like someone told you a particular contract was "silent" on the issue of assignment, and therefore it was "freely assignable." In other words, nothing in the contract addresses whether either party has the right to assign its rights in and to the contract. Under the general rules governing assignments, if a contract does not prohibit assignment, then it is freely assignable. Insofar as who assignability benefits, that is not broken down by buyer or seller, but instead by the motivations of the parties under specific facts. For example, one seller may not want a contract assigned because it agreed to something because of the specific buyer it was negotiating with (perhaps seller financing), so an assignment would be something the seller does not want but it could be beneficial to a buyer if the buyer decides that it cannot close the deal but can find someone who will so the buyer does not lose their deposit. At the same time, another seller may not care who buys the property, so long as a deal closes at the price the seller wants regardless of who the purchaser ends up being. On the buyer's end, back when property values where increasing rapidly, a buyer would want a contract to be assignable, because it could sign a contract at a lower price, then before closing assign it to someone willing to pay more and the buyer would keep the difference. In that situation the right to assign would be beneficial to the buyer, not the seller. As I said, that was back when property values where increasing rapidly, but in today’s environment, buyers and sellers both seem to want assignability just to get a deal closed, but lenders considering short sales are leery of schemes where the borrower gets back into the home with the lender receiving less than owed, so they generally want to approve a sale between their borrower and a specific buyer.