It's just a newer version. Newer versions of programs.
For example Fedora Core2 uses Gnome 2.6 and X.org X server 6.8.0.
Fedore Core3 uses Gnome 2.8 and X.org X server 6.8.1
Some improvements of X.org 6.8.0 over 6.8.1 include better drivers support. It has support for new X extensions such as X Damage and X composite (disabled by default, but it allows REAL transparencies).
some improvements of gnome 2.8 over 2.6 include usability refinements. Better mime detection. Evolution 2.0 as the default e-mail client. Support for Vector-based SVG graphics in games and such (check out the solitare games for instance. When you change the sizes of the Windows the cards change sizes automaticly to fit well. With the Gnome 2.6 if you changed the size of the windows the cards remain the same size. There is also initial partial support for things like HAL and Dbus, which in future versions will allow tighter integration of applications and allow applications to respond to hardware changes.
for instance if you have a handycam or whatever and plug it into the firewire port you could potentionally have a video editing application start right up. Or allow easier burning of cdroms without having to have administrator rights (either thru logging in as root or using suid bits). Well that's the idea, you just have the groundwork supported right now.
Just lots of little things. Of course since it's a brand new OS your going to have bugs popping up here and there. Also it's going to take a while for people to build and test new packages for it, so the application support is going to be lacking for a while.
So there is probably no compelling reason to upgrade right now. Wait a couple months until you get comfortable and then when your ready just download the cdroms and perform a upgrade to the new version. It's usually pretty painless and Fedora/Redhat makes sure that a upgrade is a real upgrade and that you will have full functionality that is provided by Fedora Core3.
Just aviod installing lots of third party RPM's from random websites and such. These will cause the most issues. Check out package handlers like
apt or yum and use that to make your life MUCH MUCH easier (still use the cdroms/dvds for upgrading OS version numbers though).
However for anybody still using fedora core1, it's definately time to ugprade. Also Fedora is on a 6 month release cycle, so keep that in mind.