In general, an octet is a group consisting of eight elements. It has a more specific meaning in several fields.
On most computers, the smallest unit of memory addressing -- or byte -- is 8 bits, so the terms "byte" and "octet" are often used interchangeably. However, the size of a byte is determined by the architecture of the a particular computer system: some old computers had 10 or 12-bit bytes. An octet is always exactly 8 bits. As a result, computer networking standards almost exclusively use "octet" to refer to the 8-bit quantity.
In music, an octet is a musical ensemble consisting of eight musicians. The two best known octets in classical music are probably those by Felix Mendelssohn (which is for a double string quartet) and Franz Schubert (which is for clarinet, bassoon, French horn, violin, viola, cello and double bass). Igor Stravinsky also wrote an octet for wind instruments (an unusual grouping of flute, clarinet, two bassoons, two trumpets and two trombones) and Paul Hindemith wrote a lesser known piece for clarinet, bassoon, French horn, violin, two violas, cello and double bass.