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Boolean searching allows a searcher to limit or expand search results in one search string. The typical operators are AND, OR, and NOT. Search terms may often be truncated by using "*," meaning all terms using the letters up to the "*" will be included in the search. Depending on the database, the operators may or may not be "nestable" by using parentheses. One of the more confusing issues with using boolean operators is that, similar to math functions, some databases prioritize the operators, perhaps applying all instances of a specific search operator before incorporating one of the others (e.g. all "AND" operations applied before any "OR" operations). For this reason, it is IMPERATIVE that you read the "how to search" section of any database or catalog that you are using.
The following YouTube video (5:20) from the University of Regina (Canada) provides an excellent introduction to Boolean searching.
Both MIT and the Rasmusen Library of the University of Alaska Fairbanks have developed concise yet informative pages on boolean searching on their library websites. Basic information is provided, along with Venn diagrams showing how search results can be expanded or limited.
Please take note of the final section on the UAF page where mention is made of how different catalogs and databases may handle boolean operators differently. Thus, when using an unfamiliar database, please take the time to read the "how to search" section.