In the middle of the Main Preferences window is a section labeled Downloads. The first option in this section, activated by default, is "Show the Downloads window when downloading a file." During a file download, Firefox will display the Downloads window which contains download progress as well as other pertinent information. If you would like to stifle this display when you download a file through your browser, simply uncheck this option.
There is also a sub-option here, disabled by default, labeled "Close it when all downloads are finished." When this option is activated, Firefox will automatically close the Downloads window as soon as all current downloads have completed.
