If you jailbreak in iOS, you can install packages using .deb files. Being a Linux user I know Debian-based distros use that file type for apt. I know that iOS is not Debian-based or Linux-based, but it is UNIX-based. Why does iOS use .deb files when you jailbreak?
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
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
dpkg-deb allows these deb files to be installed and managed easily and with little overhead, which is very important for iOS devices.