TO check if your router/modem wireless security is ON, log into your network device thru your browser by typing the router's IP address. Look for wireless settings or configuration preset shown such as the image below.
The most common IP address for routers are 192.168.1.1 or 192.168.0.1. Confirm this by your manual. Another way is to check your Network profile for your Home network which consist of your router password and ID/SSID commonly known as a name given for the wireless connection broadcast and set to connect automatically. Click on your Network icon in system tray and choose Open Network and Sharing Center - Manage Wireless Network
and look for your Router wireless network ID. If it is present, then your wifi is password protected and is only broadcast as normal to a specific range in your neighborhood. Unless they knew your password, they would have meant is just being shown as being broadcast but not able to connect. Some routers have features to check on the network status of who is using your network.