Endian-ness refers to how the 4 bytes (or 8 in the case of the G5) of a value are organized in memory. Big-endian systems are easier to debug manually (it reads like a series of normal numbers), while little-endian systems are there from older design like the x86 and 68k (it takes more time to read through numbers, as chunks are 'out of order' in left->right languages). Little-endian was easier to work with when going from 8-bit to 16-bit chips (Reading from memory was easier to implement from existing design).
Byte-swapping is changing from Big-endian to little-endian or the other way around.
Flashing firmware is taking new software, and putting it into the erasable ROM (usually a FLASH ROM, hence the term 'flashing').
The PPC is Big-endian, the x86 little-endian... and because of the larger x86 installed base, cards are designed to be little-endian. So, Mac drivers usually have to change data from Big-endian to little-endian before giving it to the card. ATi cards perform slightly worse on the Mac platform as a result (it takes time to 'byte swap').