Not really, it is more like a rental agreement. But importantly, you have the exclusive right to renew the agreement with the registry at the end of the initial registration period, so effectively you can keep the name as long as you want. Its very important that you renew your domain name each year on-time as failure to do so can cause it to expire and become available for someone else to register it.
For information regarding domains please visit our domain registrations section of the site which answers alot of these questions.
Each year you will be invoiced for your hosting and domain name. Please ensure that you make sure this is paid quickly and without delay to avoid any interuptions to service or worse expiration of domain name.