To impersonate a domain is to become (or act as) the administrator of that domain and you will be able to perform all the functions of that domain administrator on their accounts. When you click on either the impersonate or details buttons you will be transferred to the OpenAthens MD administration interface in a new tab or window as the administrator of the domain in question, or as the organisation administrator that 'owns' the personal account. When finished you should close the tab or window that was opened before impersonating any other domains or organisations.
Any actions you take whilst impersonating should, of course, be done with great care as you have the ability to break access for your customer. For information about using the OpenAthens MD interface, please see the MD documentation.