How do I change passwords for the main and secondary accounts?

I am very confused here.  I want to change the password for my main email account and it's associated secondary accounts.  When I click Virgin Media Mail settings from the Account settings page, I am asked taken to a Mailbox App password management page.  Okay so Virgin Media have changed something to something I don't understand and I don't know what this Mailbox App is.  On the same page there is a Generate new App password button - but for what app?

I am bit old school and use MailWasher Pro to check my accounts for email and delete spam accordingly.  I then use Pegasus Mail as my email client for my Virgin Media accounts and store my emails locally.

I don't want to generate a new app password in case it locks my main and secondary accounts, rendering them useless.  Especially when I don't have an app to enter the new app password.

I just want to change the passwords for my main and secondary accounts as a security practice.  What is all this about an mailbox app, where do I download it and how I did change my passwords in it?