If you are trying to troubleshoot problems with scripts not working the way you expected the log can give you clues as to where problems might exists. Likewise, you can have your scripts write to the log to help identify what they are doing. If you have selected to filter out binary files and/or less useful transactions a log of those transactions will be available here.
The proxy session log is not saved in the workbench, if you close screen-scraper you will lose the current contents of the proxy session log.