The index, also called catalog, is the main database of the site. When the index received your site, it will analyze it and add it to the active database where the search are performed. The search engine function is the one used by common surfers to find websites. It will look through the database to find the most relevant site to the query given to it. The trick to get high ranking is to understand what is relevant for the search engine.
Every search engines have their own ways to search their database.
But there are some points most of the search engines look for. The title is an major factor on most of the search engines. You should always add your most important keywords to your titles. Some search engines will also seek in the first few lines a words written in a bigger font, like a headline. Frequency is another important factor most of the search engines look for.