A VPN kill switch is a setting that cuts a device's internet access whenever the VPN connection drops, so apps cannot fall back to the unprotected connection.
Explanation
VPN connections drop more often than people notice: a phone moves from Wi-Fi to mobile data, a laptop wakes from sleep, a server restarts. Without protection, the operating system simply sends traffic over the normal connection until the VPN reconnects, and in those seconds apps reveal your real address and destinations to the network. A kill switch closes that gap by blocking traffic that is not going through the VPN. Some apps do this for the whole system; others only block chosen apps. On Android the system itself offers it: 'Always-on VPN' together with 'Block connections without VPN'. The trade-off is availability: if the VPN cannot reconnect, you are offline until you fix it or turn the switch off. A web proxy has no equivalent setting because it never captures the device's traffic in the first place. Pages you open inside the proxy tab go through the proxy, and if the proxy is down they simply fail to load. Everything else - other tabs, other apps, and WebRTC calls made by the browser - always uses your normal connection, kill switch or not.
In practice
A kill switch blocks all traffic the moment a VPN connection drops, so nothing slips out unprotected. Android builds this into the system: since Android 8, "Always-on VPN" can be paired with "Block connections without VPN". Without it, a phone that moves from Wi-Fi to mobile data can reconnect directly for a few seconds before the tunnel returns — enough for apps to send traffic in the open.
Sources: Android — VPN settings
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