Mappings in CF are different from mappings in IIS/PWS.
In IIS and PWS, you can set up Mysite.com/myFolder to point to some random folder on the C: drive. This allows you to have "virtual directories" and make a website tree that does not necessarily resemble your Hard Drive.
On the other hand, CF mappings are used for a different purpose. You can set them up to make Absolute paths to templates used when CFIncluding and CFModuling.
I.e.: You have some big CF application, and all pages should use the same look-and-feel template. In such a case (especially good for Fusebox and the like), wouldn't it be nice to have a way of including files from other folders, without calculating the relative path to that folder? Say you are in www.mysite.com/folder1/folder2/folder3/index.cfm and you want to include a file in the www.mysite.com/resources folder.
Do you honestly want to try typing CFINCLUDE template="../../../resources/MyHeaderAndFooter.cfm" ?
What happens if you move things around? That is like asking for a disaster! Therefore, set up a mapping which maps, say "/Site_Resources" To C:\inetput\wwwroot\Resources (for example), Then, wherever you want to include that file, simply write: <CFINCLUDE | CFMODULE TEMPLATE="/Site_Resources/MyHeaderAndFooter.cfm"> No more recalculation of paths when you move things around!
=====TO SUM THINGS UP====
Mappings, in both IIS/PWS and CF, are used after the folder requested, could not be physically found. CF looks for folders when compiling code to execute. IIS/PWS looks for folders when retrieving files to send to the browser.
In the sequence of events that a server follows (this is very high level!):
1) WEBSERVER processes request of file /FolderX/INDEX.CFM
2) WEBSERVER looks for FolderX inside its wwwroot folder
3) WEBSERVER finds c:\inetpub\wwwroot\FolderX
4) WEBSERVER FINDS file INDEX.CFM in folder FOLDERX
5) WEBSERVER realizes that it is a cfm and asks CF to read it
6) CFSERVER reads INDEX.CFM
7) CFSERVER discovers that index.cfm wants to include FolderY/a.cfm
8) CFSERVER Looks for a FolderY inside FolderX
9) etc. ...
You can see here that IIS/PWS mappings affect Step 2, and CF Mappings affect Step 8. That's the best way I can explain it.