Synaptic is just a program you can find in the menu's, it asks for your login password before it runs, because it does things to your system that the systems owner may do.
Under (Debian based) Linux variants like gOS all software installation/de-installation is managed with a program called "APT", but just like almost all Linux software APT isn't a GUI based program. Under Linux the graphical system (called x-windows) runs on top of of the text based actual Linux. on top of the graphical system one (or more) of many different Graphical User Interfaces (GUI) runs. In the case of gOS this is GNOME, the most popular GUI. On top of GNOME are running GNOME based applications, like Synaptic (and many others).
http://en.wikipedia.org/wiki/Synaptic_%28software%29But I just said that APT is responsible for software installs so what is Synaptic the. Well Synaptic is the GUI-frontend for APT. It interacts with the user through the GUI, but the actual work is done by APT (you can also use APT directly, by using the "text monitor"). There are other GUI front-ends for APT, for example the update manager, and the application installer "The ubuntu software center"
http://en.wikipedia.org/wiki/Ubuntu_Software_CenterSo how does Synaptic/APT work, where does the software it installs comes from. Well Linux is not a commercial system, all software is free, and comes from volunteers, or companies that donate software (like Firefox, and adobe flash and Adobe PDF reader and such). All free software is given to a group of volunteers that make sure that the software will work on different target systems (slightly different versions might be needed for different Linux distro's, or generations of a Linux distro, like Ubuntu 8.04 or 9.10), this is called "packaging for a distro", or just "packaging". They create software packages (.deb packages) suitable for the target system. These are then put on a target system specific server, called a "repository", then Synaptics can read a list of what is available from the repository (or repositories) that are suitable for your system (these are listed in "software sources" another program), and shows what is available and/or already installed. It also keeps track of "dependencies", what a piece of software needs to run, that is "libraries", or programming language support like Java, and if necessary also installs them.
Only some software (mostly from commercial companies that don't want to give the blueprints {source code} away) is bypassing Synaptics, and the repositories (but not APT). There you often have to download a .deb package directly, and start another GUI-frontend the ".deb installer" by "opening" the .deb package.
But sometimes the software authors also release software for experts, so they can bypass the packagers, if a package is not available for their (maybe exotic) distro, its then mostly in source form, so you can compile it yourself (or modify, and or package it).
No need to excuse yourself, we all are happy to help, that is the spirit of Linux.