If you mean install phpBB, you can do so through cpanel>fantastico. It will automatically install for you. But the copy in the fantastico is not the latest version.
Anyway to answer your question yes, you need ftp to upload all the files. Its the fastest way. Of course you can also use file manager to do so but it will take a longer time :noexpress
First you create a directory at the public_html where you can upload the files to. (eg you can create a directory call "forums", so your site will be
www.domain.com/forums) Then you unzip all the phpbb files and upload them to the directory.
If you use ftp all you need to do is to drag and drop the files. If you use file manager you may have to create the same directory as the unzip files of you phpbb and upload them one by one.