Boolean operators use AND, OR, NOT to limit or expand a search. (Note the capitalization. Many databases require operators to be in all caps, as do search engines like Google, which also allows for Boolean based searches.)
In other words, the search results will contain search term X and search term Y.
In other words, the search results will contain search term X or search term Y or both.
In other words, the results will not contain search term X.
Boolean operator searches can be simple, e.g., Moose AND Elk; Moose NOT Elk. Or they can be more complex and nuanced when combining operators and use parentheses, e.g., (Caribou AND Elk) NOT Moose; (Moose OR Elk) NOT Caribou.
In this very broad the Music Index search pictured below, the results will contain sources that reference jazz or blues and, in either case, will also reference Chicago.
To make even better use of Boolean operators, you can use parentheses to nest query terms. In the search pictured below, the results will include sources that address jazz AND New Orleans or blues AND Chicago.