Hi Redtom010, and Welcome to SH ;D
I have removed your other post as things get a little complicated if there are 2 open threads on the same subject.
So, a few questions first to make sure we are thinking on the same wavelength:
1. What operating system are you running?
2. Whereabouts on the taskbar is the icon - to the right near the clock or in the centre where your open windows are shown?
3. Is there any text on the icon? (Try hovering your mouse over the icon to see if a 'bubble' pops up showing the text)
4. When did it appear? You mention a download so it would be helpful to know what sort of download it was (movie, program, music file)
From your description I would guess it is an indication of a running program and if we prevent that program running then the icon will disappear of its own accord, but let me know about the problem and we can start attacking it.