WiFi Auto Reconnect simply detects when your device goes offline (i.e. you lose internet connection) at which point it turns off WiFi (if not already off), then turns it on to try to reconnect to your saved WiFi network. The app can run in the background to ensure WiFi will try to reconnect itself (you'll see the notification icon that it's enabled).

To help you understand where this app would be useful... WiFi Auto Reconnect was made to solve a problem with a phone dropping WiFi connections that needed to stay online and connected. Over time the device would sometimes lose internet connection over WiFi or the router would drop the device and it would not reconnect. This app ensured that the device reconnects to the WiFi network by itself without requiring manual intervention. This app was made as the existing alternative apps didn't keep running in the background (this one is also cleaner to look at).
You will need to ensure that the WiFi network is saved and the option to connect automatically has been checked.