Boolean Logic is based on the work of Mr. George Boole, an English mathematician of the 19th century. This style of logic consists of grouping things and then discriminating between those groups, connecting and combining and separating them to describe the set of features that are desired with a variable level of precision.
In working with this kind of Logic it is first important to understand the concept of sets. For example, in the image below the yellow colored area represents the set of all things related to Subject A while the blue colored area represents the set of all things related to Subject B.
By using the term AND to join terms within a Boolean Logic system such as article databases that which is returned are only those things which relate with both Subject A and Subject B together as represented by the Green colored area below. This is a great way to narrow your search to a specific part of a broader subject.
If on the other hand, we use the Boolean Logic OR term to combine our search terms we will have returned things dealing with A and things dealing with B as well as things dealing with both. This is a great way to broaden the search a bit and look at multiple synonyms - such as vehicle, car, auto, and automobile as we can't be completely sure which of those terms have been used in any given article on the same subject. Again the regions in question have been colored Green in the image below.
Finally, you can use the Boolean Logic term NOT to exclude parts of a subject that are known to not be relevant. By excluding terms with a NOT you will return results that only have the term you want not the term you don't want, even if they occur together. In the image below we have searched for A NOT B, so we will get back the Green shaded region, not the Blue or Bluish shaded regions.
Alternatively, in the image below we have searched for B NOT A, so we will get back the Green shaded region, not the Yellow or Bluish shaded regions.