Piwigo requires a web hosting to run. For a photo gallery solution with all included (installation, hosting, backups), or if you simply want to try Piwigo with no installation, you may consider opening a free trial account on Piwigo.com.
A graphic library: ImageMagick is recommended (better performances and image quality) or GD which is often bundled with PHP.
an FTP client software will be required to upload the files (netinstall or full package) : Piwigo team recommends FileZilla as FTP client software, because it is free as Piwigo is, and compatible with Windows, Mac and Linux.
Piwigo is also included in Softaculous or other auto-installer system, if available on your hosting : that way you don't need any FTP client software, but you might need one later.
Enough disk space for your pictures : by default, multiple sizes of your pictures will be generated in directory _data/i.
On some hosts, multiple PHP versions are enabled and you need an .htaccess file with a specific instruction in order to enable PHP 5. Contact your hosting company to know exactly their procedure.
The Netinstall itself produces such an .htaccess file on some hosting.