Web analytics (often referred to as just analytics) is the measurement of visitor behavior on a website, for the purpose of improving that website. Popular analytics software includes Google Analytics and WebTrends.
Why use analytics?
Measure your visitors - without an analytics solution, it is impossible to get a reliable indication of how many visitors a website has, and how they behave.
Improve your goals - analytics allows you to measure and optimize your website for specific goals, such as buying a product or filling in a contact form.
Available for free - Google Analytics is a highly featured analytics solution that is available for free. Adding basic analytics to a website is a trivial task.
More advanced analytics solutions - like Hotjar - can actually record the behavior of your users and replay it to you like a video. These tools are extremely useful for optimizing your websites and web applications.
Further reading
Web analytics – Wikipedia