For each domain there are two parties: owner (sometimes called holder or registrant) and registrar. At certain circumstances it may be the same person but in most cases they differ. The basic difference is that the owner owns the domain and the registrar manages the domain.
Domain is a very specific product. It has to be set properly to fill its function (present the website). Most of the owners are not capable to set it themselves and that is when registrar comes in. Domain registrar is mostly a company where the owner hosts his website. For a person (webhosting company) could manage the property of another person (domain owner) it is necessary to formally proclaim that it has right to do so (otherwise, abuse could occur). In the normal life such situation entails a trust deed, but in the webhosting world there is the status of the registrar.
By finishing the order you acknowledge that the domain can be managed by the registrar to whom you pay an annual payment for the domain.