How Search Engines Rank Websites
This is a primer on how a search engine like Google works. Trying to keep it simple.
Google sends out automated programs called robots, or spiders, or bots. The bots crawl the web hopping from one link to the next as they find them on web pages. For each page a bot comes across it stores a copy of its contents into the main index that Google uses to retrieve search data. It scans all the text elements on the page and uses this information to determine what the page is about.
When a person searches for a word, or phrase, Google then scans through its index and finds all the pages that contain that word or phrase. This often retrieves millions of results. Now Google must determine a ranking by relevance. This is quite complex. More so than is summarized here.
Where, and how often, a particular keyword, or phrase, occurs on a page adds to its relevance. Placement of the keywords in the domain name, page URL (the full address to that page - www.domain.com/keywordpagename.html), page titles, heading titles, in linked text, in bolded, italicized, or underlined text, etc. As well as how often it is mentioned in the body of the text (keyword density) all play a small role in creating relevance.
Besides the text on your pages, your navigation structure and page layout will influence how the spiders crawl through your site. Poor navigation can lead to spiders not being able to find your internal pages. Excessive use of graphics or flash animation often mean very little text exists on the page, or does not exist in a format that can be read by spider bots.
These are all elements that can be manipulated to gain better rankings. But this manipulation must be done properly. Google frowns upon things like keyword stuffing. If you stuff the keyword in too many times, creating an un-naturally high density, the page could get penalized, or worse, banned from the index. Keyword densities this high also become unattractive for human readers of the page contents.
Those are the on-page elements used for ranking. Google also relies heavily on off-page elements. Namely linking. A link counts as a vote. A site that attracts more links from other sites is deemed to be more important and will often rank higher.
But it is not simply a popularity contest. And not all links are weighted equally. Some sites carry much more weight than others and will pass more link weight to you. Certain poor linking strategies can even harm your rankings. You'll need the right kind of links from the right places to get the best results.
Within a link, Google also reads the linked text, this is called the anchor text of a link (the usually blue underlined text you would click on). This text is often descriptive of the page it is linking to. Including a mix of your target keywords in the anchor text of your links is beneficial.
Other factors include the age of the domain name, the country the web-server that is hosting the domain is located in, and others.
Google's latest algorithm update maybe starting to include something called Latent Semantic Indexing, LSI. This tries to take into account the semantics of language and multiple terms that mean the same thing, as well as words and terms that have a tendency to occur together in content for particular topics. Using a mix of different variations on your main keywords, such as plurals, ...ing's, etc., as well as other elated terms, can help in this regard.
So that is the basics of how a search engine determines how pages get shown in its results. This should help you understand a bit better and help you direct specific questions regarding your website.
More on how to get to the top of Google here, and why search engines are so important.
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