I can change my account’s password but I don’t know how to change the password of the other one. I don’t know what this password is for too. What is this password for ? How to change it?
It is the password to unlock your encrypted LUKS container. Without it, you cannot boot into your OS. It is recommended to use device encryption so that your whole data is encrypted, no matter who you are. Without it, your data would be openly readable.
In order to understand what you see there you could start by searching for “disk-luks” which is printed on your screen. Some helpful links:
Arch Linux wiki entry on device encryption
How to change your LUKS password
I just wrote a post about disk encryption in PureOS. If you’re interested in some more background it contains some links to further informaton about the function and use of exactly that password you’re asking about.