If you have your own website you can add a search box to your website for your users and use that to increase your own Search Engine Optimization and also use it for keyword research. In the back end, Google provides you with statistics on the number of times people search. You can also see what they are searching for. So if a particular search query is popular in your market then you can be one of the first to know that. You can use that information to improve the Search Engine Optimization on your website. You can also use it help you come up with ideas for future pages and websites.
Here’s an example. Let’s say you own a website dedicated to teaching people how to chop and pick out the best firewood for their home furnaces and chimneys. If you notice that there are a lot of searches for cherry wood and you don’t have any web pages on your site dedicated to cherry wood then you can create a page for cherry wood. The next time someone searches for cherry wood, they may find your web page instead of someone else’s. If they don’t, tweak the page to improve your Search Engine Optimization.
Note that this is only going to work if you have your site search settings set to search the whole web. If your searchers can only search your own site then the results are not going to include your competition. It will be like not having site search at all.