1. <character> 0, ASCI character 48. Numeric zero, as opposed to the letter "O" (the 15th letter of the English alphabet). In their unmodified forms they look a lot alike, and various kluges invented to make them visually distinct have compounded the confusion.
If your zero is centre-dotted and letter-O is not, or if letter-O looks almost rectangular but zero looks more like an American football stood on end (or the reverse), you're probably looking at a modern character display (though the dotted zero seems to have originated as an option on IBM 3270 controllers). If your zero is slashed but letter-O is not, you're probably looking at an old-style ASCII graphic set descended from the default typewheel on the venerable ASR-33 Teletype (Scandinavians, for whom slashed-O is a letter, curse this arrangement).
If letter-O has a slash across it and the zero does not, your display is tuned for a very old convention used at IBM and a few other early mainframe makers (Scandinavians curse *this* arrangement even more, because it means two of their letters collide). Some Burroughs/Unisys equipment displays a zero with a *reversed* slash. And yet another convention common on early line printers left zero unornamented but added a tail or hook to the letter-O so that it resembled an inverted Q or cursive capital letter-O.
2. To set to zero. Usually said of small pieces of data, such as bits or words (especially in the construction "zero out").
3. To erase; to discard all data from. Said of disks and directories, where "zeroing" need not involve actually writing zeroes throughout the area being zeroed. One may speak of something being "logically zeroed" rather than being "physically zeroed".