Hi @MKR17 ,
Currently, within most of Microsoft Cloud services, it use Azure Active Directory (Azure AD, Microsoft's cloud identity service) as the authentication way.
More details about authentications within Office 365 cloud service, please check the following article:
https://docs.microsoft.com/en-us/office365/enterprise/about-office-365-identity
When you sign in PowerApps first time, it would ask you to provide your email address, then password. When you click "Submit" button, it would send a http request to Azure Active Directory (Microsoft's cloud identity service), Azure Active Directory check the credentials you passed, if correct, return a Access_Token back to your client and your Client store the Access_Token within your browser.
After that, your client would send another http request along with the Access_Token to Azure Active Directory server, Azure Active Directory server check the Access_Token, if match, you would be authorized with permisson to access PowerApps.
Next time, you sign in PowerApps, you do not need to provide username (email) and password again, you could send an http request to Azure Active Directory server along with the Access_Token directly.
If you do not maintain our AD copy in microsoft cloud and authenticate our credentials within our network, I afraid that you could not able to login to PowerApps in cloud.
Best regards,
