Hi FranMatt,
I'll take a stab...
1.) Kernel panic (
http://en.wikipedia.org/wiki/Kernel_Panic), is commonly referred to as the "OS X Blue Screen of Death." Your computer encounters an serious/fatal error in a line of code, either in a software operational or hardware request that it cannot perform. To avoid proceeding further and possibly creating more problems for it it "kernel panics" and asks you to restart.
A panic log is generated on your computer that would tell an engineer or technician what exactly happened (why, when, where).
A Kernel panic is typically an indicator that something is wrong with your computer, the software you're using or the hardware peripheral that you've just plugged. For example, if every time you go to run Microsoft Office the machine "KPs" then it could be something with that application which is causing the issue and would require a reinstall.
Kernel panics are obviously something you don't want, and they're typically easy to avoid (for the most part). Install approved software from manufacturers, run updates, use approved drivers for hardware, etc. But they can happen, at any time for any reason.
2.) Kernel task (seen as kernel_task in Activity Monitor) is a system level function that essentially controls your operating system. If you Google it you'll get all sorts of responses, ironically, many about issues with it and the MacBook Air. My understanding is the kernel_task is a low level system function that essentially communications all the GUI "stuff" to the underlying system, with some back-and-forth. When it balloons and begins to hog a significant portion of RAM and CPU the system becomes virtually unusable (like a Windows memory leak).
I've seen some users on the discussions state that kernel_task is also run as an idle command when their MBA gets hot in an effort to cool down the system. I'm unsure if there's any documented evidence to support that theory from Apple engineering but from my experience the more than task grows in resource allocation the warmer my machine gets.
Recently, 10.5.5 system updates and a separate MacBook Air have been released to identify performance issues with this particular model. It's unclear exactly what was changed, how it was changed and if it really worked (or was necessary). You'll get mixed reviews from people here, with some saying it made things better, others saying nothing changed, and a few saying it actually made things worse.
Personally, I've had my Air since the 3rd week they were made available and have had fantastic luck with mine. It came with 10.5.2 and I've run all my updates when they've been made available and have never suffered performance problems, core shutdowns, etc. I also recently got a second Air, via my employer, that came with 10.5.4 and have also had nothing but fantastic luck and performance.
