What's needed to let player create and access its account in Pygame?

I've been learning Pygame for a quiet long time. Now, I'm managing to let players create accounts for the game and connect to them if they're playing online.

I've seen some game developers storing players' data in text files, yet that's a very classic way and it's unsecure ! So I thought about databases ...

However, I think I'm misunderstanding how databases work in general. In fact, I was thinking of them just as servers but after doing some Google researches, I realized they're not. Let's talk about the SQLite as an example. (as i just learned the SQLite3 python module's basics on the fly).

I thought it stores data in a server or in 'clouds' (like Apple iCloud) but then I realized it just stores it on the computer disk, and this won't enable players to connect to their accounts if they're using the game from a computer that's different from the one they used to sign up for example and that's a possible case and I want to cover max cases that can happen while connecting to the game in order to ensure a good player experience with the game.

So, is there any way to ensure a good connection to the game with any device ? And do you think I have to use the socket module ?

NOTE :

Keep in mind that the game itself isn't multiplayer and doesn't need Internet connection. However, I want the players to be able to connect to their accounts from any device just to be able to save their progress in the game.

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