In a nutshell, AppleJack is a command-line utility and series of scripts for running repair tasks in Single User Mode when a bootable startup disc in not available. It's great for those times when all you get is a blue screen and no GUI startup, and need to troubleshoot and repair the problem, but left your complete CLI reference book in your other suit.
To use it, bring up Single User Mode by holding down Command-S at startup and then when the prompt is available type applejack. Use the menu provided or select 'auto pilot' to perform all of the basic tasks, such as filesystem and permission repair, cache clearing, and more. There is an 'Expert mode' available by typing 'x' at the AppleJack prompt to do more operations on the hardware and user accounts. Documentation is provided in a Man page; type man applejack for that.
This version supports 10.4 and up. Since Apple usually changes things under the hood with each major OS release a tool like AppleJack has to be updated for compatibility, so older versions didn't function properly in 10.6.
For more details, there was an excellent review of the previous version on Macworld. This will give you a good feel for this tool.
[crarko adds: I tested this, and it works as described. I swear by AppleJack, and am delighted it's finally 10.6 friendly. Just remember it needs to be installed before you have trouble, and not after the fact.]

