As you may know, dpkg -i package_name.deb is used for installing software on debian systems. But dpkg -i does not install the package dependencies.
Example: I want to install packageX.deb, but it is not in the default repositories so I can not install it with apt-get or aptitude, so I download it from the internet, by wget let’s say.
$ wget https://linuxg.net/package-example/packageX.deb
$ sudo dpkg -i packageX.deb
But this installation cannot be done successfully because it depends on a packageY, that is not installed in the system (we assume that packageY is in the default repos).
So, next you have to install packageY with apt-get install and next to install with dpkg packageX.deb:
$ sudo apt-get install packageX.deb
$ sudo dpkg -u packageY
If you want to avoid all this installation package trouble, install a .deb package with gdebi.
Gdebi is a smart tool capable of installing .deb packages, and using the apt-get package manager in the background, to install the software dependencies.
First, install gdebi: sudo apt-get install gdebi
$ sudo gdebi packageX.deb
This will try to install packageX.deb with dpkg -i , find out that it needs packageY (or other dependencies), installs packageY and the other dependencies needed (with apt-get -f install), and install the packageX.deb with dpkg -i.