"site" to another easily with this technique. What the Domain Mapper lets you do is point parked domains to specific spots on your site tree as a starting point for that domain. An example:

You own myBaseDomain.com as well as mySecondDomain.com and myThirdDomain.com.

You setup a site tree that looks like this:
Home

+secondSite
    +About
    +Contact
+thirdSite
    +About
    +Contact
+About
+Contact

By default, your site runs at myBaseDomain.com so assuming pretty URLs is turned on, the following links work.
myBaseDomain.com/about
myBaseDomain.com/contact
myBaseDomain.com/secondSite
myBaseDomain.com/secondSite/about
etc.

Now follow these steps:
1) Using cPanel or your other server management software, you need to "park" mySecondDomain.com on your account. Once you do this any traffic coming to mySecondDomain.com will get redirected to myBaseDomain.com

2) Go to the Domains tab here, and enter mySecondDomain.com in the domain name path and pick the "secondSite" page.

Now any traffic coming to the mySecondDomain.com will see the content of the secondSite page, and their url will look like:
mySecondSite.com

When they click links, they will continue to have the same domain in their URL field, but WILL see the full path of pages, so for example:
mySecondSite.com/secondSite/about


ABOUT USERS:

Note if you make a user account, be it admin or regular on any one of the urls, you will have effectively made an account on all of them. You will still have to login each time you visit a new URL however, as the user session is tied to the root domain. If you are making edits to the site, it probably makes most sense to login to myBaseDomain.com as you will be able to visit each page in the site without the URL changing and logging you out. 

Domain Mapper Doing nothing in concrete5.4.1+ ?