Many search engines (including Yahoo, Google, Bing and others) provide search suggestions, which are based on popular searches other people make that are related to a word or words that you enter. When Search Suggestions are enabled, the text you type into the search box is sent to the search engine, which analyzes the words and displays a list of related searches.
This is one of these things that is useful on a phone but probably more trouble than it’s worth on the laptop. I tend to use the Awesome Bar to quickly search my browser history (to the point that I no longer bother bookmarking anything), so adding search suggestions would probably be more confusing that enlightening for me.
Still, it’s easy enough to switch it on and off again, so there will be no problem if I change my mind.