Wi-fi is a bit of a different beast than wired communication. With a wire, the signal is protected: It travels from the port to your device, with no chance for people in between to see what's being sent. Wireless signals are sent over the open air. This means that these connections are far more vulnerable to being hacked by people between the router and the device.
You may even be connecting to an attacker's device directly, rather than a router, allowing them to channel the Internet through their device and take whatever information they find interesting. Even with your own home router, people who can get access to your connection may be able to view your personal files, take your passwords, or even do things that are illegal using your network, making you part of the crime.
This includes your address, phone number, location, or anything else you'd rather keep private. Once you've made sure you're not leaking your own information, it's a good idea to use the private browsing mode on your computer or regularly clear your cookies when you're using the Internet. Companies use cookies to track where you've been and can often piece together this information to reveal who you are.
Another important thing to think about when keeping yourself safe online is cyberbullying. This is like the bullying kids might experience at school, except that it happens online. You can't always prevent this from happening, and it's not the victim's fault when it does. But you can fight it by reporting the messages to the websites they use, blocking them on websites and apps, and not responding to them.