AND is used to narrow a search. If you connect two or more terms with AND, all of those terms must be present in your results. Many if not most databases automatically insert AND between any terms you type into the search box.
An example of AND's usage:
Imagine a database of burgers--Burger Search Complete. It contains burgers with mayo, lettuce, and tomato; burgers with mustard only; ill-conceived burgers with tartar sauce and pudding--you get the idea. You want to search for certain types of burgers, say, ones with mustard and ketchup. You don't care if there happens to be mayo or pickles or anything else on there too, just so long as mustard and ketchup are both there.You would phrase your search as in the picture below:
Now every burger result that you get back will definitely have mustard and ketchup on it.
A Venn diagram may help to explain:
Only the middle, overlapping portion of the graph would be included in the search. It represents all the burgers with both mustard AND ketchup on them.