Boolean operators are connecting words (OR, AND, and NOT) that link two or more keywords or phrases in your search. As their name implies, Booleans act like operators (=, +, -) in a database, telling the search tool to look for your keywords in a specific way.
The first operator, OR, is like telling the database "I want Coke but Pepsi is fine, too."
OR will find records containing one or both of your search terms. This makes it especially useful for finding variations of the same topic which may be talked about in multiple ways. For example, the search phrase colonization OR colonialism will retrieve articles that use either the term "colonization," "colonialism," OR both. Without the "OR," you might get a lot of results that use one term, but miss out on results that use another, older term referring to the same phenomenon.
In contrast, using AND as your Boolean operator is like telling your waiter at the restaurant "I want diet Cherry Coke. I'm not willing to settle for normal Cherry Coke or plain diet Coke. It has to be specifically Cherry AND diet."
AND specifies that you only want to see results containing all your keywords together. For example, if you're looking for research about British colonization specifically, you would use the search British AND colonization.
Finally, NOT is a search term you won't have to use very often. To keep using our drinks metaphor, NOT is like asking your waiter for a diet Coke and stating that you will NOT take diet Pepsi as a replacement.
NOT will find records containing the first term/phrase but not the keyword(s) following the NOT. This is most useful when the term you're searching for is often paired with a specific example which you want to avoid. For example, if you're searching for research on British colonization and you don't want to look into the British occupation of India, you would want to add NOT India to the end of your search.
Nested searches are so named because of their "nests" made up of parentheses. These nests are used to separate different topics or pieces of your search from one another. In essence, they work the same way that parentheses work in Mathematics: the Boolean operators within the parentheses are applied to your search first, and then they are searched with any terms or phrases outside of the parentheses. For example:
British AND (colonization OR colonialism)
will search for BOTH the term British AND either the term colonization or colonialism. Without the parentheses, your search would look for "British AND colonization" OR just "colonialism." Then you would end up with a lot of resources on colonialism, with nothing to do with Britain.
Adding nests to your search basically allows you to do multiple searches all at the same time. Instead of searching for "Britain AND colonization," "British AND colonization," "Britain AND colonialism," and "British AND colonialism," you can simply use this nested search:
(British OR Britain) AND (colonialism OR colonization)
The key to a good nested search is to get creative! Try different terms, add more or take some away, and most importantly, keep a record of what combination of terms works the best. You can try the exact same search in multiple databases to try and find alternate resources you can add to your research.