The Byte Order (also known as endianness) describes the sequence or order of bytes. They are arranged to form larger values, which comes in handy when storing the file or sharing it. The Byte Order is important to be known since bytes (and bits) can be represented in two different ways, ordered from the most significant or the least significant one.
The big-endian Byte Order is the more common one of the two. Mixed cases of the two exist as well (mixed-endian, middle-endian).
It may happen that files are created on a machine or computer that creates files using big-endian, for example. These cannot be correctly interpreted by machines reading little-endian only. Thus, the Byte Order of a file provides information which way the file can be opened or processed.