Definitely is a ServerFault question, I work in software packaging and deployment for a large company and this is what we do.
An MSI file is an installer built for the Windows Installer system, if you have at least Win XP (might even work with Win 2000 SP4) then you'll have a version of the Windows Installer already installed. Its used by things like Windows Update and most commercial (and a lot of non-commercial) software. Most Setup.exe's these days just call an MSI to do the real install.
If you're just installing on one PC then you just double-click the MSI and install as normal just like your average setup.exe installer.
The real magic of an MSI comes when you need to install it on a lot of PCs with little to no effort.
Go to the Run box in Windows and type "
msiexec" this brings up the basic command line options for the Windows Installer, and are all options you can use with your MSI to get it to install with no user interaction, totally silently or with various levels of logging enabled.
Eg to install skype.msi silently with default settings you'd use something like this command line:
msiexec /i \\servername\share\path\skype.msi /qn
You should be able to take that command line and put it into whatever your company's deployment method is, whether its Group Policies, MS SCCM (or the older SMS), Novell ZEN, Altiris DS, etc or even something as simple as inserting it in a login script.
Where the real magic of MSI installs comes in is when you don't want to use the default install options, but want to miss out components, install to a different path, put in a company config file and so on. You can use tools to create MST files (MS Installer Transform files) these tell the Windows Installer to follow the MSIs instructions but with differences that you specify. You'd then use a command line like this:
msiexec /i \\servername\share\path\skype.msi TRANSFORM=\\servername\share\path\mycompanysconfig.mst /qn
There are a lot of MSI Transform creators on the market from people like Altiris, Symantec, Acresso, and so on. Most of them have cut-down free/trial versions of their software that you can play around with and can be extremely powerful.