In computing, to start your computer running. The term derives from the phrase to pull oneself up by one's bootstraps (from The Adventures of Baron Munchausen).
Your BIOS runs a BootStrap Loader, which can start code running from the boot block of a CD, a floppy disc or a HardDisk. The code that runs is called a BootLoader (which may 'chain' other bootloaders) which then starts an OperatingSystem.
Historical Note: The term derives from 'bootstrap loader', a short program that was read in from cards or paper tape, or toggled in from the front panel switches. This program was always very short (great efforts were expended on making it short in order to minimize the labor and chance of error involved in toggling it in), but was just smart enough to read in a slightly more complex program (usually from a card or paper tape reader), to which it handed control; this program in turn was smart enough to read the application or operating system from a magnetic tape drive or disk drive. Thus, in successive steps, the computer `pulled itself up by its bootstraps' to a useful operating state. Nowadays the bootstrap is usually found in ROM or EPROM, and reads the first stage in from a fixed location on the disk, called the `boot block'. When this program gains control, it is powerful enough to load the actual OS and hand control over to it.