They are a basic building block of all library and Internet search engines, and learning how to use them will give you a great deal of control over your search, and improve the quality of your results.
The following diagrams explain how each operator works.
AND narrows
Finds only the records that contain both keywords.
Use AND between keywords that represent different ideas.
OR expands
Finds all the records that contain either keyword.
Use OR between keywords that represent the same idea.
NOT excludes
Records must contain the first term and exclude the second.
Use NOT to exclude an irrelevant keyword from your results.
You may notice that most Advanced Search pages are designed to help you group (or nest) your keywords to produce more complex (and efficient) search statements.