To begin, when you log into cPanel, you can see a section for 'FTP Accounts'. This allows you to create an account that will connect to your account and allow you to upload files with. You can use FileZilla to input your username and password that you created through the 'FTP Accounts' section.
Alternatively, you can use the built in File Manager which comes with cPanel. Simply click the upload button with File Manager (usually at the top) and you will be taken to a new screen. Browse for the file you wish to upload, in your case, the MyBB ZIP file. Once uploaded, you can then select the ZIP file in File Manager and extract the contents. (you may have to move the files to home or your preferred folder).
After that, you can then begin installation. I'd also suggest creating a database aswell as MyBB will need this to connect to.