Boolean operators include AND OR NOT. They are often built into the search interface as options, but sometimes you just get a simple search box and have to put them in yourself.
AND - is probably the most common. I was all articles that include BOTH of the terms. Often just putting more than one term in a box invokes an and search.
OR - is one that we often forget about (and Google often does it for us) but in a world of keyword searching, it is critical to include all the variations that you want to retrieve. When you search in English, sometimes you need to tell the database to search for EITHER spelling such as theater OR theatre. Another example would be to search for synonyms such as: kids or children.
When you search in Japanese you will want to look for variations - an easy example is 漫画 or マンガ or まんが. If you don't ask for all of them, you might miss some really good stuff. Sometimes you can cheat and just search by manga in romaji, but then you will also miss the articles that don't include English abstracts and titles.
NOT - is very useful when you know that you are going to get a big number of hits in a related field and you want to exclude them. An example of this would be 日本文学 NOT 翻訳
Now, when you start to combine them together you can get into sophisticated searching. According to Boolean logic, the operators inside the parentheses are handled first and then the result of that is processed against the next operator. So, in this example （ひきこもり OR 引きこもり） AND ゲーム I am asking the search engine to look for either spelling of hikikomori and then find the articles that also mention the word ゲーム. If you still had too many hits and wanted to exclude some of them, you could put parentheses around the first set and add the next operator (（ひきこもり OR 引きこもり） AND ゲーム) NOT ネット.