The "seeing" refers to the atmospheric turbulence etc, particularly the upper atmosphere. I think it is mainly influenced by the jet stream, which is above the cloud layers. So if the seeing is "good" and if you could blow away all those pesky clouds, you would be able to get nice sharp star images.
I usually look mainly at the cloud predictions (total cloud). If it is clear then I check "seeing" to see whether it is likely I will get good images.
"Transparency" refers to how much muck is in the air. This is mainly cloud, so "transparency" largely mimics the cloud patterns, but it could be dust in the upper atmosphere- so you can have no cloud, and good seeing, but lousy transparency: that is when you will be OK looking at bright objects, but faint fuzzies will be even fainter.
Conversely, you could have no cloud, good transparency, and lousy seeing: that's when planets look crap, stars scintillate like mad, but faint fuzzies aren't too bad. (And if you check the jet stream then, you will usually find it is very strong.)
There's more to it than that, but hopefully that makes some sense. No doubt Andrew Cool, who developed the site, can explain a lot more if you contact him.
The other thing to note about SkippySky is that I believe it generally uses data that has about a 20km sample size or resolution, so it has its imperfections. It is as good as you can currently get with the data that is in the public domain.
The other site I often turn to is from the Brisbane Storm Chasers website, with real-time satellite images:
http://realtime2.bsch.au.com/vis_sat...art=&stop=#nav
-it is a great one to cross-check with SkippySky.
All the best,
Dean
PS: I notice that IceinSpace has imperfections too: it is telling me that where you are in the Sunshine Coast is currently 14,544km from me in Adelaide... In which direction I wonder?