I can't exactly differentiate photoshop, fireworks and Illustrator... but I shall give it a try...
In my own opinion...
[b]Illustrator[/b]
Illustrator is a vector-based postscript drawing program. This tool is most commonly used for vector editing like creating logo's and stuff... that you need to make shapes as individual part to create an image.
[b]Fireworks[/b]
is an adobe application which is for bitmap and vector graphics editing...
fireworks is much focused on vector editing like Illustrator. Vector objects in Fireworks can be resized with no loss of quality, just as in Adobe Illustrator. I can't exactly differentiate Illustrator from Fireworks coz they are much more alike in terms of editing vector objects.
And lastly...
[b]Photoshop[/b]
The most commonly used tool for bitmap editing or image processing.
It's ideally suited for creating, modifying and outputting digital images of a photographic nature.
It is much more different than those two adobe applications since this tool is used for image enhancement.
If you don't know what's a Bitmap and Vector graphics...
I think it needs much more explanation to you...
Hope that helps