Even though Akeeba Backup is designed as an effortless way of backing up your site, it is only good up to the point of having a backup archive. Restoring it is a pretty much different story.
Without Kickstart you would have to download the backup archive file to your computer, extract it, upload all the files to your site via FTP or SFTP (with 5000+ files per site this is slow), then go through the restoration process, and finally remove the installation directory.
Most of this process is the same for every backup restoration. The only place where human intervention is truly required is the restoration process part. Moreover, transferring thousands of files over SFTP or, worse, FTP is orders of magnitude slower than transferring big archive files. These are the problems Kickstart is designed to solve.
Kickstart extracts the backup JPS, JPS and ZIP archive files directly on the server you want to restore your backup on. The only thing you need to perform a restoration is Kickstart and the archive file(s). You just need to upload kickstart.php (renamed as something that does not contain the terms kickstart, ks, or akeeba) and your archive to the server, visit its URL (e.g. http://www.yourdomain.com/example.php), select the archive, wait to be extracted, go through the restoration process, click the cleanup button and your site is up and running. All unnecessary files –Kickstart itself, the backup archive and the restoration script– are removed.
In case your files and directories ownership and permissions are mixed up Kickstart can write files using FTP, SFTP or our Hybrid mode. The Hybrid mode solves a problem known as "permissions hell" where different files and folders are owned by different users, making it impossible to write to all of them either directly or through FTP. In this case Kickstart intelligently decides which method to use (direct write or FTP) on a file-to-file basis.