Your Internet connection appears to be working. You can safely close this window and continue using your device.
elementary OS automatically checks your Internet connection when you connect to a new Wi-Fi network. If it detects there is not an Internet connection (i.e. if you are connecting to a captive portal at a coffee shop or other public location), this window will appear and display the login page.
Some networks can appear to be a captive portal at first, triggering this window, then actually end up connecting. In those cases, you'll see this message and can safely close the window.