Simultaneously, the first client will begin sending some of its file pieces to the second client and likewise the second client will send some of its file pieces to the first client. As the network grows, the distinction between client and server blurs, with the network simply evolving into a grid of file transfer nodes all working together to accelerate the file transfer process.
This approach provides dramatic performance improvements and is highly reliable due to the massive redundancy of file sources in the network. At the same time, more of the bandwidth burden of the system is offloaded from the single server onto the rest of the network, allowing delivery of huge files to large audiences without a large amount of bandwidth at the origin server.
For a visual of the process, check out the the Swarming Simulation."