How is booting in to Windows in safe mode different from a normal boot?
In Windows XP, Safe Mode "uses a minimal set of device drivers and services to start Windows" (KB315222). Importantly, no network drivers are loaded, and Microsoft's own vga.sys display adapter driver is used instead of the one that is designed for your hardware by its manufacturer. This can get you out of a situation where you set display properties incorrectly causing your display adapter not to work.
See the following Microsoft Help and Support web page for more information about Windows XP's Safe Mode and its variations: http://support.microsoft.com/kb/315222.
This Microsoft TechNet article has more detail about boot options as implemented in Windows 2000: http://technet.microsoft.com/en-us/library/cc976736.aspx.
Raymond Chen wrote an column in the July 2007 issue of TechNet Magazine describing the behavior of Safe Mode in Windows 95: http://technet.microsoft.com/en-us/magazine/cc138008.aspx.
My understanding is that it loads only the minimum drivers/settings needed for a very basic windows boot. There are other options though such as starting with networking support (adding more drivers and settings to the boot), or the command prompt as as shell instead of Explorer.
Safe mode helps you troubleshoot a windows installation with bad driver and/or configuration settings.
L0C0B0X is correct. Here's more info:
The basic idea is to allow starting Windows with a minimal configuration of driver software and advanced settings in order to troubleshoot problems which make a Windows installation unusable (unstable drivers, problems with auto-starting software ...)
In "safe mode" just basic graphics drivers are loaded, enough to display the user interface in a low resolution, access to drives and Windows configuration, and very little else.