Port 3306: MySQL
Port 3306 is the default port for MySQL and MariaDB databases.
What runs on port 3306
MySQL and its fork MariaDB listen on TCP 3306 for database clients. They back a large share of the web, including most WordPress sites. Applications normally talk to them on the same machine or a private network.
On a home network
NAS boxes (Synology and QNAP both offer MariaDB packages) and home servers running self-hosted apps may listen on 3306. Consumer devices do not.
If port 3306 is reachable from the internet
A database should never be reachable from the internet. Exposed MySQL servers are brute forced constantly, and there have been campaigns that log in, copy the data, delete it and leave a ransom note. Many installs listen only on localhost by default, so an exposed one usually means someone changed that.
How to check whether it is open on your network
On the server, check the bind-address setting and whether a router rule forwards 3306. RECON's Exposure Check tests it from outside.
To find out whether port 3306 is open on something in your home, and whether the internet can reach it, the app scans your Wi-Fi from your phone and checks your public address from the outside. It says what it checked and what it could not. Get RECON for iPhone — one-time purchase, no account, nothing leaves the device.