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A script is a set of instructions for something else to run. For example, .bat files are DOS scripts. There are shell scripts for every operating system I know of.
The boot of a computer is the startup sequence. This is everything from when the power button is pressed to when the OS finishes loading.
If you put these two concepts together you get the boot script. This is a set of instructions that are carried out while the computer is booting. In DOS, this was autoexec.bat, but it was replaced by other things in Windows. In linux there are the rc.d scripts that are executed at different run levels durring boot and shutdown. On a Mac, this would be the Startup Items. All of them do effectivly the same thing. Run one or more scripts at the time of booting.