Each google search results consists of 3 main items: The title, the description and the URL link. Lets start by looking at the Title.
Title of Google Search:
The title of the google search result by the major search engines (Google, MSN and Yahoo) is directly determined and pulled from the websites' Title HTML tag. This title does not appear within the website's content (unless of course the website duplicates the Title within their content) rather, it shows up in the top of the browser window, giving that page on the website a Title.
As shown in this screen catpure below:
Thus, its imperative that your website pages all have effective Page Titles so the search engines can index your website efficiently.
The Description of Google Search Result
The description that appears within the search results is very similar to the Page Title. The search results description is being pulled from the websites meta description value. Within each web page, you can define a descripiton for that page. This description is not found in the web pages content presented to the user, rather it just lives in the code behind the website. The reason for the description is to tell the search engines what your website page is about. Generally the description is a 1-2 sentence brief description about that web page.
So when the search engines crawl your site, they first read your Title, then your description and so on.
So to summarize, since the Title and Description don't neccessarily live in the content of the web page, often times when you find a search result and read the descripiton, you will not find that exact copy on the web pages content.