This is a situation that arises when your Shotgun site is configured to use Single sign-on (SSO).
When SSO is enabled, Shotgun periodically needs to connect to your Identity Provider (IdP) to ensure that your user information is up-to-date. This happens at login, and approximately every 4.5 minutes. It stops when you sign out.
In some special cases, the IdP may impose restrictions on the way the user information can be updated. When this occurs, we have to use a secondary window to achieve this goal. This is the situation that you are seeing.
Please keep this window opened. Should you close it, Shotgun will re-open it when needed.
You may be asked to allow Shotgun to use pop-up windows. Shotgun will notify you and will not allow you to proceed until pop-ups have been allowed. Every browser has a different way of enabling pop-ups.
Usually browsers try to make this task easy, and there will likely be an icon in the address bar:
Or a new button at the top of the page:
When you sign out, the smaller window should close automatically. If not, you can go ahead and close it.