Core Image is built into the OS. It's not an application, it's an infrastructural part of Mac OS X that some applications (almost none at the moment) take advantage of.
as before stated there is no way to "open" coreimage, but you can check to see if its supported on your machine, by going to your system profiler and looking at the specs on your video card, where it should tell you supported or not
none "need" it to work currently but most notably right now the "ripple effect" when you open a new widget in the dashboard is one effect that is a result of coreImage
if you install the Developer Tools that came with your Mac you will find a little app called "Core Image Fun House" that demonstrates some of what Core Image is capable of.
People mis-understand CoreImage so much! CoreImage is available on Macs that do not have full GPU support for it. In this case CoreImage falls back to the CPU. This can happen on Macs with full GPU support if CoreImage thinks that this will give higher performance.
It is possible for the calling app to ask CoreImage if a particular effect will run on the GPU or CPU. This enables apps (like Dashboard) to not display an unnecessary effect (say the ripple) if it will run on the CPU.
You can get a slightly technical overview of CoreImage here.
If you want to play around with CoreImage install the Developer Tools and play with Quartz Composer. You can even save any nice compositions as new screen savers 🙂