there's a built-in option to connect to your Google account and sync it to Drive — which then lets you pull it up on any other computer where you're signed in by clicking on that same option there
By default, that data is all stored only locally for maximum privacy.
My Notes is just a giant open text field for your notes — once you collapse down its menu, which can be done with the handy hotkey of Ctrl-Shift-F.
having as a new tab isn't really the best way to use this though
go to
chrome://extensions/shortcuts
and set your own hotkey for opening it up is the best way to use this imo