What exactly are Paas, Hosting and SaaS ?
Wikipedia to the rescue.
PaaS - Platform as a service
SaaS - Software as a service
Hosting
Heroku is not a DNS registrar. You can however buy domains elsewhere, such as Godaddy and add them to your Heroku app. By default you are given a free my-app-name.herokuapp.com domain. After you have purchased a domain, to "point it at heroku", you'll need to add a CNAME record which points to your my-app-name.herokuapp.com domain.
When you purchase a domain, you'll need to host the records on a DNS server. Some registrars provide free DNS hosting, others charge extra for it. You can purchase DNS hosting from Amazon Route 53 for $0.50 per domain / month. To use Amazon, you would need to change the domain's name servers to Amazon's.
Domain > Name Server > Hosting provider / PaaS.
One limitation of using Heroku is that you cant use apex domains. You must use a subdomain eg. www.example.com instead of just example.com. This is a DNS limitation - you can't have CNAME records on the apex. It must be an A record. Amazon Route 53 is one of the few providers that allow virtual CNAME records on the apex. It's basically an A record that is frequently updated. Each time your Heroku app sleeps due to inactivity, you may be given a new ip address when it restarts.
Further reading on DNS on Wikipedia.
ps: Happy New Year!