Does saving the cpanel on my site mean anything. I am currently using host gator as my web hosting network, but I am considering into switching into another one, but I am worried I will lose all the content on my site. I took a backup of my cpanel just in case but I don't know how these things work.
It is up to the server admin delete your old content. It is unethical keep the files of clients that have moved to another server so if you are switching to another, download all of your files, whether as a backup tar or each by each before changing your nameservers Otherwise you can usually will be able to access your site, while it is not cancelled, this way: http://your-hosting.com/yourusername or http://IP-HOSTING-NUMBER/your username.
i have moved many sites for people, i'll get a complete backup from cpanel and move all the content to the new server, when i am satisfied that all is well, i delete everything from the old server. i don't leave anything for the old host.
from cpanel, you can backup your site content and database , then move and set it up on another hosting, not so simple, but it can be done.
Don't cancel your old hosting plan until your are 100% sure you have everything you need from the account (files and databases). Make sure everything is working correctly on your new host before you change your nameservers too.