What It Is
MySQL is a database system, meaning software that stores and organizes data so a website can use it. It arranges information in tables, much like spreadsheets, and lets the site ask questions such as "show the five newest blog posts." WordPress uses MySQL or MariaDB, a closely related system that works the same way for most purposes. Your host runs it on the server, and you rarely need to touch it directly.
Why It Matters for Your Business
For a business owner, MySQL matters when you move hosts, restore a backup or troubleshoot an error. A message like "Error establishing a database connection" on a WordPress site means the site cannot reach MySQL, perhaps because the database server is down or a password changed. Knowing the term helps you describe the problem clearly to your host or developer.
Good to Know
Tip: keep your database login details in a safe place, such as a password manager, and never share them in plain email. Hosting control panels usually include a tool called phpMyAdmin for viewing the database, but editing data there by hand can break a site, so leave changes to someone experienced.