The byte has been universally accepted as the atomic entity of data storage for some decades now. But beyond that, you're on your own. Integer numbers larger than 8 bits are stored in several bytes, and there the common ground ends.
In the little endian format, the least significant byte (LSB) is stored first. So the hexadecimal number $FACE would be stored as $CE $FA. The big endian format stores the most significant byte (MSB) first, resulting in $FA $CE.
Most CPUs have a preferred or native format. Data in the other format can only be accessed with a performance penalty. As a result, everyone tries to use their platform's native byte order. As you'll see later on, some formats are defined to use a specific byte order, while others can occur in either one. This will be noted as appropriate.