What is free and what is not
- Free: the WordPress software from wordpress.org, thousands of themes and plugins in the official directories, and the right to use, change and move your site wherever you like.
- Paid, always: hosting and a domain name. Every website needs both, whatever platform it uses.
- Paid, sometimes: premium themes, premium plugins (forms, SEO, backups, ecommerce extensions), page builders and the pro versions of free plugins. A typical small business site uses two to five paid tools.
- Paid, usually: a developer to design and build the site, and maintenance after launch. You can do both yourself, but most businesses do not have the time.
Why it is free
WordPress is developed by volunteers and companies that make money from the ecosystem around it, under a licence (the GPL) that guarantees it stays free and that anyone can modify it. That licence is also why you own your WordPress site in a way you never own a site on a hosted builder: the code is yours to take to any host or any developer.
WordPress.com is different
The confusion usually comes from wordpress.com, a commercial hosting company that runs the same software as a paid service with plans from free to several hundred dollars a year. The free plan shows ads and uses a wordpress.com address; the business features are on the higher plans. See the difference between WordPress.com and WordPress.org.
All in, a self-managed WordPress site costs a few hundred dollars a year to keep online, plus whatever you spend on building and maintaining it. The website cost page covers the build, and how much website maintenance costs covers the upkeep.