What's sometimes confusing is that there are 2 different ways to use Wordpress. Wordpress.com is the free blogging platform. Wordpress.org is the home of the version you host yourself on server space you rent.
So if you want a free blog you can use Wordpress.com. The drawback is that they don't really allow commercial sites. The popular alternative is Blogger.com - which does allow ads, affiliate marketing., etc so long as you don't over do it.
My preference is for a self-hosted version of the Wordpress.org version which has two advantages in my opinion. First, it's much more powerful and flexible. Second, you have control. If you want to run a personal blog, free is fine. If you want to run a business blog, the free platforms could change the rules tomorrow and put you out of business.
Hosting will cost you $5 or $6 a month. Your own domain will cost you about $11 a year. The Wordpress software is actually free. So if you're doing it on a commercial basis you've got a set-up where you make the rules for less than the cost of a pizza per month.
What's so special about Wordpress? We could be here all day answering that one. In a nutshell it's the power and flexibility - which has made it not only the most popular blog platform but the foundation of many thousands of non-blog sites.