what is admin password

Unable to install apple macOS Montessori,

Are you asking about what an admin password means, or that you have forgotten your admin password?

The admin password is the passcode to open the computer. The first user account on a Mac will be an administrator account, and subsequent user accounts on the Mac will either be a standard account or administrator accounts.

If you have forgotten your Mac password see If you forgot your Mac login password.

Montessori, a prominent name in education, is less well known in the field of computer science, although she may have been an early but unknown pioneer - given that she died in 1952. I suspect that you meant macOS Monterey.

+1 !