Some data represented in hexadecimal form, usually with the same characters included (if they're printable). Here's one example:
ca fe ba be 00 03 00 2d 00 a1 08 00 58 08 00 59 08 00 5a 08 Êþº¾...-.¡..X..Y..Z.
00 6d 08 00 6e 08 00 6f 08 00 70 08 00 71 08 00 73 08 00 75 .m..n..o..p..q..s..u
08 00 76 08 00 79 08 00 7b 07 00 78 07 00 8b 07 00 8c 07 00 ..v..y..{..x........
8d 07 00 8e 07 00 8f 07 00 90 07 00 91 07 00 92 07 00 93 07 ....................
00 94 07 00 95 0a 00 10 00 3b 0a 00 16 00 3b 0a 00 18 00 3b .........;....;....;
...
Those were the first few lines of the hex dump of the hex dump program itself. =) Unprintable characters are represented as dots.
Hex dumps are particularly useful if you need a readable form of some arbitrary binary file.
in *NIX, od is a good program for generating hex dumps.
See also: hex editor, Copyright Violations 101 : Posting Boot Sectors on Everything (fairly silly)