Here's my interpretation:
Persistence: This setting determines whether or not the CSS will allow persistent HTTP connections. i.e. will a browser be allowed to maintain a single TCP connection for multiple requests, or will it be required to open an individual TCP connection for each bit of content. In web-server speak, this is sometimes referred to as "keepalive"
Flows: A flow is CSS speak for a TCP connection. Once a flow is established, an FTP connection for example, the CSS will maintain that flow for the duration of the connection. The CSS will not loadbalance traffic "mid-flow" except under unique circumstances, when a service goes down and remap is configured for example.
Sticky: The various sticky configurations come in to play when you want to have all connections from a particular client go to a particular service. This is most often accomplished with cookies, or sticky tables which track a clients' IP addresses. There is a limit to the size of the IP address table, so cookies scale better for web content.
