I can't say that I have always used stats when working on the Internet. But when online marketing became my main profession, stats turned into the lover I never had. We were joined at the hip!
There are very few hosting companies that don't provide some sort of basic statistical program in their package. And if one doesn't have this luxury, there is always Google Analytics. Whether you pay for it, or accept the free basic version, you can find something that will help you decipher your main audience's demographics, what they're viewing, what systems they're using, etc.
If you're just starting out, you may be wondering, "Why would you want to use all that?" Because I can glean a wealth of knowledge on what my audience wants to see.
On my website you're viewing currently, my main audience is the United States and then Europe. But, I have another website that I use extensively and after the United States, I was surprised to discover that Russia is my second highest audience.
With a little research and ingenuity, I can keep the Russian market by always including their culture and time zone into some of my articles. It just takes research on my part.
I also know that a whopping 67% of my followers are on mobile with a Qt Browser system. Chrome comes in second at 15%. This let's me know that my webpages had better be mobile compatible.
Facebook gives me the majority of my views and referrals (between 3-4pm), yet very few, if any, of my customers come from Facebook. (I know this by asking my customers how they found me). After that, Pinterest, LinkedIn, and Google searches round out the guests.
And this morning, someone found me by Googling the word "Mercy". There's a surprising stat and truthfully, I don't know what I'll do with it. It's just a fun fact to know.
Your stats will tell you what you need to focus or stop focusing upon. They will give you feedback as to your performance and what the people need.
Stats - they help you improve your job so that you can give your audience what they need.