What are important tasks to know about using cPanel for web hosting?

Well, I know this will sound pretty generic, but it depends on the purpose of the site.
For instance, back when there were CMS tools like phpNuke, which tied in well and supported phpBB2 forums, security and administration were made easy to manage by the tools and utilities offered through phpNuke.

To be more cPanel specific, and regardless of purpose, IP Tracker is great, for reasons of security; i.e; block IPs known to exploit not just your site but other sites; can be totally proactive in this sense. Great way to feel secure about a site with so many bots and hackers now day.
Remote MySQL is nice, haven't seen that before. Great for any merchants, or manufactures that can easily add a new product straight from there phone.

Bandwidth manager/Visitors is a great way to not just view your site traffic, but manage it as well, though more for sites that have downloads available.

In the end, in my opinion it totally depends on the site's purpose. If someone is using this to just blog for whatever reason, many of those tools are irrelevant (no real need for DB, Bandwidth, Encryption, SSH access, ect.,).

Hope this helps.