AxCrypt 2 asks you to sign in to your account, which AxCrypt 1 did not. We now use a single sign on model where the same password is used to sign in to our servers and to protect your files. The password that you’re being asked for is the password to your account, which you probably created when you first installed AxCrypt 1.
If you do not remember the password to your account, you can always reset it. This is not a way to recover encrypted files! It’s only to allow you to sign in to the AxCrypt app and web. The new password will be used to encrypt new files. Go to https://account.axcrypt.net/Home/PasswordReset to do this, or you can also go there from AxCrypt with File | Options | Password Reset .
If you open files encrypted with a different password than your sign in password, which often is the case directly after upgrading to version 2, you will be prompted for that original password. If the file was encrypted with version 1, it will then be automatically upgraded to version 2 and to use the new sign in password which means you won’t be prompted again for the old password.