Wifi Switcher will switch to the Wi-Fi network with the strongest signal from your remembered networks.
It runs constantly in the background. When the Android system scans the Wi-Fi networks, Wifi Switcher will check to see if any of your preferred networks has a better signal strength than the one you're currently connected to. If it finds one significantly better then it will switch to it.
At home I have a Wi-Fi access point downstairs and another one upstairs. If I go upstairs I stay connected to the one downstairs but the signal is much weaker. This app will automatically switch you to the stronger Wi-Fi connection.