cPanel is a web control panel that allows easy management of web hosting related tasks. Management is done via web browser. With cPanel you can manage FTP accounts, databases, access logs and statistics, upload/download files, have integrated File Manager, can setup cron jobs, add new domains, subdomains or parked domains, setup e-mail and lots of other tasks.
Ftp accounts can be setup with cPanel. New accounts or modify existing accounts, permissions can also be configured, like which folder-only access will be allowed, how much data can be transferred and similar.
New databases can be created, and database users (with permissions) can be added. You can see overall database info and statistics, and delete/edit users/databases.
Depending on the configuration by the hosting provider, you can access current server stats (memory usage, cpu processes), access program paths and versions, server load and other server info. For websites there are couple of tools like latest visitors (shows 300 latest of all your sites). Raw logs, bandwidth information, error logs are also accessible.
File manager is an excellent tool for uploading, downloading, modifying files online. It is very easy to use and supports drag and drop interface, zip extraction, file/folder permission edit and other. It is my favorite and most frequently used tool.
There are lots of other tools available that can ease tasks. There are also plugins available. For example with the Fantastico you can install quickly and easy popular web applications: wordpress, drupal, joomla, phpbb, galleries and others.
Currently cPanel is the most popular control panel. Competing with cPanel are Plesk (windows), hsphere, lxadmin, webmin and others.