The main advantage that comes from turning Wi-Fi off on a cell phone is a reduction in power consumption and a corresponding boost in battery life. The Wi-Fi radio in a phone can be powered down or turned off completely when Wi-Fi is disabled.
It is not always wise to turn off Wi-Fi, particularly in situations where mobile data may be used as a result. Mobile data such as 3G and other long-range communications require far more battery power than short range Wi-Fi data transfers.
Modern mobile operating systems are designed to recognize when Wi-Fi is not needed and tend to put a handset's Wi-Fi radio into a power-efficient state when the functionality is not needed. When looking to save on battery power, manually turning the Wi-Fi off comes below many other recommendations, such as activating a built-in power saver mode or reducing screen brightness settings.