<mathematics> Number base eight. The octal number representation uses the digits 0-7 only, with the right-most digit counting ones, the next counting multiples of 8, then 8^2 = 64, etc. For example, octal 177 is digital 127:
digit weight value 1 8^2 = 64 1* 64 = 64 7 8^1 = 8 7* 8 = 56 7 8^0 = 1 7* 1 = 7 --- 127Octal representation used to be widespread back when many computers used six-bit bytes, as six-bits can be conveniently written as a two-digit octal number. Since nowadays a byte is almost always eight bits long, the octal system lost most of its appeal to the hexadecimal system. Octal is still found in the C programming language and its descendents where it is commonly to represent characters, as in 'A' = '\101', 101 being octal for 65, the ASCII character code for 'A'.
For a brief discussion on the word `octal' see hexadecimal.