Moving from one host to another

Just want to ask one probably simple question.

Let's say I have now my website hosted with Hostgator (shared plan) and would like to move to another host (knownhost VPS).

So if i just backup my entire site and upload all files to my new host (via file manager), does it mean that my site will work after nameservers get updated? Or I still need to do something with my current databases?

A hostgator shared plan will use cpanel. If you move to a VPS that has cPanel you can backup from cpanel on HG and upload that backup to cPanel on the new host and it'll work like it did before. You should however move to a host that offers to freely move your site. If they cannot offer such a basic service they probably won't be a good host.

Knownhost is a managed VPS provider. This means they should take care of the moving part for you. Open a ticket with them providing them you HG cPanel login information and they should do the rest for you.