What does it mean to reformat a computer?

Actually we usually speak of reformatting the hard drive on the computer. The computer's hard drive is the internal drive that has no removable media. On it will be stored the operating system (such as Windows or Unix), most of the applications (programs) you use, plus all kinds of data files. A hard drive is a disk (or set of disks) with a magnetizable coating on which a recording head can write information. Each kind of computer and operating system has its own way of formatting that information, but they all write in concentric circles, grouping the information into smaller blocks or sectors. Before data can be stored on a hard drive (or any magnetic disk, actually), it must be formatted. This process magnetically creates the writeable areas on the disk. To reformat the disk means to recreate these areas, refreshing the disk to a new state. A full format permanently erases everything on the disk as part of the process. A "quick format" may be available, which will not bother to erase everything but will just mark everything as erased, with pretty much the same result. (Custom programs may be able to recover some erased information, but only if it has not yet been overwritten.) Generally, when you reformat a hard drive--at least, the primary drive on the computer--you want to make it bootable, installing on it the components of the operating system that allow you to run your computer.