How is a node chosen in a Swarm cluster when Read/ Write requests are sent from the application?

The PAN (primary access node) does a multicast and receives bids from the other nodes. The node with the "lowest cost" bid response is chosen to do the operation and the client is redirected to that node, the SAN (secondary access node) – unless the PAN is the lowest cost and a redirect is not necessary.
While the exact computation of the bid is a DataCore trade secret, it can include items such as:

Available disk space
Available memory
Current activity (I/O) already in progress

The overall goal of the bidding mechanism is to have the Swarm storage cluster automatically manage your data and to utilize all of the nodes in the cluster. It is a dynamic load balancing mechanism for all user requests and it is an ongoing background process that will move data as necessary to keep the cluster optimized.