It has two option for create a portal. One is parent portal, another is child portal. What the difference between these kind of portals. Only the different domain name or something difference? For example, if I have two portals.

www.MyDomain.com, www.MyDomain.com/New.

Is there any relation between these two portals? Could anybody help me?

All portals are treated the same except that one is designated as the default portal which is usually portal 0, but that can be changed in Host Settings.

The only difference is in the way you access them as Mitchel pointed out, and that child portals need to have a physical folder created to hold the child'd default page, but all that page does is redirect back to the main default.aspx page with a querystring to allow the proper tab for the homepage of that portal to show.

Here is some more reading on the subject:

Use SiteUrls.config to clean up the DotNetNuke Child Portal Url