Simply speaking, "dual radio" means a device like a Wi-Fi access point has two radios in it. This allows the access point to provide connection to the 2.4 or 5 GHz frequency bands. One radio connects devices to 2.4, and the other radio connects devices to 5 GHz.
A dual radio device also functions as a translator between devices that operate according to different protocols. For example, a dual radio device can allow a laptop (802.11) and Bluetooth device (802.15.1) to communicate with each other even though they operate using different IEEE standard protocols.