I'm not sure what language you are using, but some languages differentiate between a normal boolean operator and a short-circuit operator. For example, the following are normal boolean operators in MATLAB:
C = or(A,B);
C = A | B; % Exactly the same as above
However, this is a short-circuit operator:
C = A || B;
The short-circuit syntax will evaluate the first argument and then, depending on the value, will potentially skip over evaluating the second argument. For example, if A is already true, B doesn't have to be evaluated for an OR operation, since the result is guaranteed to be true. This is helpful when B is replaced with a logical operation that involves some kind of expensive computation.
Here's a wikipedia link discussing short-circuit operators and their syntax for a few languages.