Kickstart is a PHP executable file ( script ) which extracts JPA, JPS and ZIP archives. It can be used over the web (from a web browser) or directly from the CLI.
Typically, it's used to extract the backup archives created with Akeeba Backup and Akeeba Solo on a new server or when the administrative interface of your site is no longer accessible. The actual restoration does not take place through Kickstart, though. The restoration script is included in the backup archive itself. Kickstart merely extracts the archive and lets you run that restoration script. At the end of the process Kickstart lets you clean up with one click which removes itself, the backup archive and the restoration script.
Additionally, Kickstart can be used to install various PHP CMS and popular scripts such as Joomla!, WordPress, Drupal etc. It can also be used to extract ZIP archives with numerous or big files that cannot be extracted otherwise. Just make sure your ZIP files are using the Deflate compression method.
Kickstart is also localisable, meaning that it can display itself in your own language. All you have to do is to upload your language's translation INI file in the same directory as Kickstart.