what is stealth mode

Type "stealth mode" in the Finders Help menu, and you'll get the answer to your question:

If you’re concerned about security, you can use the stealth mode to make it more difficult for attackers to find your computer. Stealth mode is available if you have the firewall turned on. When stealth mode is turned on, your computer does not respond to “ping” requests and does not answer to connection attempts from a closed TCP or UDP.

Regards,

Clinton

If someone says "anyone there?", in stead of replying "no-one but us chickens boss" in stealth mode we say nuthin'. In addition, if we are a router, we don't broadcast out identity periodically.

If no-one can see you, they can't attack you. This is good.

OTH, if your router isn't broadcasting its SSID, you have to know what it is to connect to it. Bad for you, good for strangers. Also, if you are not responding to eg ping requests, the router may decide that you aren't there any more and drop the connection.