Perhaps this is a better way of describing the effect of domain mapping.
root blog subdomain. All the posts and pages in your root blog here at wordpress.com have URLs that contain "wordpress.com". All the blog content belongs to that root blog and the Google PageRank and Technoarti rank and authority belong to that blog. They cannot be transferred. And your posts and pages have been indexed and are in Google under those URLs conyaing "wordpress.com".
If you do not purchase domain mapping and set up a wordpress.ORG install for your domain, then when your readers use Google to locate posts or pages and click the URL containing "wordpress.com" the links will produce a "404" (page not found). They will not connect to your posts ans pages.
If you do purchase domain mapping then when readers click the old root blog URLs they will be seamlessly traferred to the correct post or page on the domain.
WordPress.org software is free of charge. It's the web hosting that costs. For quailty hosting figure an average monthly total cost between $10 to $25 generally, but that all depends on storage and bandwidth requirements.