Base 8 system for representing
numbers. Octal has a long and dignified
history, starting from the days of computers with
word sizes
divisible by
3 (like the
PDP 10, and others (like the
PDP 11) in which the
machine code instruction format was based to a certain extent of triplets of
bits.
Octal is also the ideal format to describe a UNIX file permission: For each of User, Group and Others you can specify read, write, and execute permissions. If you write the bits, they are rwxrwxrwx, so octal makes sense here. Most people use 0644 for their non-executable files, which translates to "read and write permission for me, read-only permission for others (inside and outside my group)".
Historically, 8 and 9 are also considered octal digits by UNIX hackers, due to some bug in an old C compiler.