Big-endian systems and the smallest memory address
If the map of memory bytes were arranged from left to right in incremental address order, the smallest address is on the left.  The largest address is on the right.
Let's say you are storing the 32-bit value, 19088743, which is 0x01234567 in hex, at address 0x1000.  Hence, the 4-byte value will span over the 4 bytes at memory address 0x1000, 0x1001, 0x1002, and 0x1003
In big endian, the 01 is stored at 0x1000 (the smallest address) and the 67 is stored at 0x1003 (the largest address).  Exactly how you would think of it if you had never heard of little endian.
In little endian, the 01 is stored at 0x1003 (the largest address) and the 67 is stored at 0x01000 (the smallest address).
Big Endian and Network Byte Order generally mean the same thing.
Big Endian
|===================================|
| 0x1000 | 0x1001 | 0x1002 | 0x1003 |
|-----------------------------------|
|  0x01  |  0x23  |  0x45  |  0x67  |
|===================================|


Little Endian
|===================================|
| 0x1000 | 0x1001 | 0x1002 | 0x1003 |
|-----------------------------------|
|  0x67  |  0x45  |  0x23  |  0x01  |
|===================================|