I'm a CS student, and I've learned that (at least in most cases) sessions are stored in cookies, that's why you keep logged in even after a computer restart.
I wanted to see it with my own eyes, so I made a simple experiment. I just logged in a popular website (e.g. youtube, gmail, facebook, etc), and typed document.cookie into the the console then received the content. After that I opened a new browser, went to the same site, and paste the cookie with this command document.cookie = .... I refreshed the page, but it didn't work. What am I missing? Based on my knowledge, it should work.