They are only needed for firefox sync.

That is the password for the Sync account and the sync (recovery) key that Firefox stores in the Password Manager.

You should backup the sync key if you haven't done this yet.

chrome://weave (Mozilla Services Password)

   chrome://weave (Mozilla Services Encryption Passphrase) 

I have this on my saved passwords, I freak out, and delete both without knowing what they were or copying them, neither known what was that about. Can somebody explain me what was this about? I do not know anything about computers by the way!

If you set up Sync and create a new Sync account or connect to an existing Sync account then Firefox stores the credentials (name, password, and Sync key) in the Password Manager to make it possible to connect to that account when you start Firefox. If you remove those entries in the Password Manager then Sync will stop working and you will have to set up Sync again.

• https://support.mozilla.org/kb/what-firefox-sync
• https://support.mozilla.org/kb/how-do-i-set-up-firefox-sync
• https://support.mozilla.org/kb/how-do-i-manage-my-firefox-sync-account