The window displays all information sent to and from the server. It will also show any errors that occurred during the transfer. The drop box at the bottom left allows you to look at the logs for each connection associated with the transfer. By default, only one connection is used. If the "download acceleration" feature is enabled, then two are used.
The log can be saved to a text file by clicking the "Save" button. You will be prompted for a file name and location to save to.