Looks like no-one wanted to help you.
I had to get my head around this as well, because some of the code examples actually misread the information, which contributed to some serious number jumping.
>> is a shift.
You need to think of 8 bits of data (1's or 0's). ie 11001100
if you >> 2 it becomes 00110011
when you &1 it does a bitwise comparison with 00000001 and the result in this case of the shifted data is 00000001 (or simply 1, or true)(if you had done it before shifting the result would be 00000000)
So in reality they are actually only interested in checking if 2nd bit in the buffer is a one, and then adding the value the data at that position represents.
The same as the next line is checking the 3rd bit.
In my opinion the two values should be reversed, as according to the wiki link below bits 3 and 2 represent AX 1 and 0 respectively.
ie I believe it should be :-
if ((nunchuck_buf >> 2) & 1)
accel_x_axis += 1;
if ((nunchuck_buf >> 3) & 1)
accel_x_axis += 2;
i found some good info at http://wiibrew.org/wiki/Wiimote/Extension_Controllers#Nunchuk
and of course at http://www.arduino.cc/playground/Code/BitMath
As I said be careful as some code posted (earlier) is using the wrong bits to determine things, and ends up with strange results.