The three major elements of a search engines are: the spider, also called the crawler; the index or catalog; and the search engine which displays the results of your query in your browser.
The spider visits your web page, indexes it, and then follows links to other pages within the site. This is sometimes referred to as being "spidered" or "crawled." The spider returns to the site every so often looking for changes.
The index is a giant database that contains a copy of every web page that the spider finds. When a web page is changed, then this database is updated with the new information.
Sometimes it takes a while for pages or changes to be added to the index. Therefore, a web page may have been "spidered" but not yet "indexed." Until it is added to the index, it is not available to searches by the search engine.
Search engine software sifts through the millions of pages recorded in the index to find matches to a query and ranks them in the order of what it believes is most relevant. Different search engines often produce very different results.