Why are .deb files used in iOS?
Jay Freeman ("saurik") is the developer of Cydia and brought Debian APT to iOS.


  The iPhone … is running a pared down Mac OS X with its standard complement of a FreeBSD-based userland over a Darwin kernel.





  For distribution, I have chosen Debian's APT


Source: http://www.saurik.com/id/1

These elements together delineate .deb files as the container for the package to be installed.


  In the world of Debian APT/dpkg, anything you can install is a "package". These packages exist in the form of .deb files


Source: http://www.saurik.com/id/7

dpkg-deb allows these deb files to be installed and managed easily and with little overhead, which is very important for iOS devices.