Begin by logging in to cPanel.
Under 'Mail', select 'E-Mail Accounts':
Next to the appropriate mailbox you wish to modify, select the 'Password and Authentication' option:
Beneath the mailbox option, a new section will appear asking you to enter a new password and confirm it in the box below. Once you have entered a new password into both boxes, you may then complete the process by clicking on the 'Change Password' button.