Hello, I am kind of newbie in WordPress and website making in general. I started recreating an older WordPress website and after some plugin update, WordPress fell in fatal error, so I decided to reinstall latest WordPress version thru web hosting, the only thing I am afraid of is losing some files from WordPress, my webhosting warned me, that re-installation will delete website database. I don't really know, what the database is, but I downloaded it to my computer, to make sure I won't lose it. Can anyone help me and told me, what the database really is? Thank you!

Most hosting providers provide backups, so you can roll back to the previous version in which your site is working fine.
> Can anyone help me and told me, what the database really is?
This tutorial on the project website will explain it more comprehensively than the comment I was about to type:
https://learn.wordpress.org/tutorial/the-wordpress-database/