A search engine is rather like the shopper in the above example. It sees the title on each web page and determines whether this would be a good result to return based on its text. If you search for 'Hi-Fi' it is highly likely that some of the results returned will have 'Hi-Fi' in their title.
To be found using the search engines you should optimize your website for a set of keyword phrases. These keyword phrases should be included in your title tag. Suppose I was a website selling Hi-Fi systems, then I would like my website to appear in search engine results when searching with the phrase 'Hi-Fi systems'. If I include 'Hi-Fi systems' in my title tag I will increase the chances that the search engines will find the page and my ranking will be higher. Of course you are not limited to adding only one keyword phrase to your title, I would recommend two perhaps three but be careful not to make it too long. Also remember make it easy to understand and descriptive for a human.