SSH not safe?

[kalpana]

Hi,

I am a new beginner and my plan is to establish secure SSH and disable root login on my Ubunto server.

I followed this video and I am able to SSH into the server:
https://www.youtube.com/watch?v=bYfQbr7vPag&t=189s

To my big surprice I also tried from another PC and was also able to SSH into the server even if the private key was not on the other PC?? I was asked for the password and after entering it I was in.. I tought it was not possible without a private key on the other computer?

What am I missing?

Best regard, J