When this pop up occurs (at what level of security you want) can be set by you. Then the admin rights are momentarily active for this instance. The pop up does not require authentication (password) but simply clicking OK or Yes. What happens is each time an action requires admin rights, either the action is denied (you don't see anything, it just won't work) or a pop up displays. OK, so your user account is set as an Administrator, but the admin rights are not active. Someone who is MS certified can likely give a better explanation and is welcome to post one. I'll do my best to explain it as I understand it. MS added the UAC feature to make this happen as a default, so you are the admin but running with user rights While this may be best practice, it is not what users do. People should run as a user and then when needed, log out, log in as the administrator or otherwise invoke the admin rights. Because of course, when running as administrator, the machine is wide open.
This is not recommended because software can do harmful (virus/security) installs as well as you installing helpful stuff. MS, knowing that many users give their day to day user account Administrator privileges.