I have deleted the emails in my Horde/Squirrelmail. But my cPanel does not reflect any changes..
To free up more space in your cPanel, you can either delete the emails or website files.

1) If you deleted the emails in the webmail program: Horde/Squirrel mail, those emails will be stored in the trash folder. In order to free up more space, you also need to permanently purge them from your account. Also, you need to empty your spam box if you have enabled SpamAssassin.

2) To delete website files, you may go to "File Manager" or "Legacy File Manager" to delete the files. After deletion, you also need to empty trash can.