The enhanced security parameter will auto-disconnect you from the handshake-server after the first peer connection is established (Publishers only are disconnected; not viewers). In effect, this makes it impossible for the server to request future handshakes from you, and hence no more future peer connections.
The feature also makes the connection activity verbose, letting you know when someone starts watching your stream and when that viewer disconnects.
The security mode also limits the max number of viewers to just one viewer, and if they do disconnect, they cannot reconnect. No one can actually; you will have to re-setup via a page refresh to let someone try connecting again.
This can help prevent someone from destroying a live stream due to accidentally screen sharing the streamID to the public.
The handshake server has no way of talking to the publisher after the stream starts. Fully decentralized once initialized.
The publisher cannot be spammed by "Watch Stream" requests if the invite link gets shared accidentally
The publisher can clearly see when someone has joined and when someone has disconnected
Increased security and privacy, with just some minor added inconveniences.