I came accross the term on World of Mathmatics:
http://mathworld.wolfram.com/Addition.html
What does it mean?
Since the refer to processors, I assume they are talking about the way computers do math.
The simplest is called a ripple carry adder. This type of adder adds the way you do, it adds the two numbers together, and if there is a carry, it gets added into the next number, and it works from right to left.
Example: Suppose you are adding the numbers 101 and 111 in binary. You add the first digits together (1 and 1) and you get 0 plus a carry. Then you add the second digits together, and you get 1 plus 0, plus the carry, which again is 0 plus a carry. Then you add 1 and 1 and the carry, and you get 1 plus a carry, so the answer is 1100, if I did my math right (in decimal this is 5+7=12, by the way).
The problem here is that the “carry” has to ripple from right to left as the logic is solved, which takes time in a computer. Each addition bit takes a certain amount of delay for the transistors to do their thing, so if you can avoid having the bits on the left side wait for bits from the right side to complete, you can make the whole thing a lot faster. One way to avoid the wait is to do what’s called carry lookahead. This is special logic that simply looks at the two numbers being added, and determines what the carry is going to be instead of waiting for the adders to determine what the carry is going to be. That way the bits on the left don’t have to wait for the bits on the right to complete before they can do their addition.