Hello 3ch0,
First, I have to admit that book mess up a lot what AND/OR/XOR is. It's a simple concept that is hidden in that text line
About ORing, well, I guess the the author wants to say OR-ing (verb finished in -ing) (that磗 english i suppose

). So, that's the same as saying: "Apply the OR operator..."
My explanation about this:
OR = binary add
0 or 0 = 0
1 or 0 = 1
0 or 1 = 1
1 or 1 = 1
AND = binary multiply
0 and 0 = 0
0 and 1 = 0
1 and 0 = 0
1 and 1 = 1
XOR = exclusive OR
0 xor 0 = 0
0 xor 1 = 1
1 xor 0 = 1
1 xor 1 = 0
So, using this 3 operators you can play with the bits in a registry/memory as you like. For example, suppose that you have in the EAX register a value. If you want to know if that number is odd or even you can make the following:
and eax, 1 ; will leave the bit-0 untouched to check if even or odd
.if eax == 1
; we are odd!
.else
; we are even!
.endif
Hope this helps