Relating to the end of a computer representation of a multi-byte number. A byte is a sequence of 8 bits, stored at an address in memory. Oftentimes a value will have to be stored in several bytes.
Big endian is where the most significant byte is stored at the lowest address, and the least significant bit is stored at the highest address. This is the mode of systems such as IBM RS6000, the 68000 series, and SUN.
Little endian is where the least significant byte is stored at the lowest address, and the most significant byte is stored at the highest address. This is the mode of systems such as DEC Alpha and Intel x86.
So, if one camme accross the following two bytes used to store an unsigned double-byte integer:
One could not know whether the value represented is 1 or 256, without specifying the endianess.
Files which store multi-byte values cannot be read directly on systems using a different endian-ness to the one on which they were written; but the extra complexity is normally handled by application software.
Some hardware, such as MIPS, is said to be "bytesexual" which means that it can be operated in either mode.