%Caelum is a plug-in/library for %Ogre targeted to help create nice-looking (photorealistic if possible) atmospheric effects such as sky colour, clouds and weather phenomena such as rain or snow. It is composed of a number of small mostly self-contained components and a big Caelum::CaelumSystem class which ties them all together in an easy-to-use way.
For more information see the big %Caelum thread on the ogre forum:
http://forums.ogre3d.org/viewtopic.php?t=24961
The thread is very long; you should try reading it backwards.
There is also a page on the ogre wiki (might be out of date):
http://wiki.ogre3d.org/Caelum
See CaelumDemo's source code; it should contain some minimal initialisation and tweaking. CaelumLab is more complicated and can be used to visually tweak different sky elements.
There is no %Caelum "SDK"; the recommended way to use it is to build it yourself.