Mugsy, Hotrod basically answered the question you asked me. His fire hose to garden hose comparison is good. From your description of what happened it sounds like the one connection was the problem, and likely will be again.
I think the poor connection was acting like a resistor, causing the current flow to go up, while also reducing the voltage and making the lights dim. Any time anything acts as a resister, whether its a poor connection, too small wire, a bad switch or an actual resister, amps will go up and voltage will go down.
15 amps seems small for a headlight circuit, but I don't have the actual current draw in my head.
Headlights are often protected by a circuit breaker because if they fail, its almost always going to be dark (otherwise you would not have turned them on) and if they don't come back on you could have an accident because you can no longer see.
I've heard arguments both ways as to whether that is a good idea...
A fuse or circuit breaker should be sized to protect the wire and switches in the circuit. The wire should be sized to provide full voltage at the needed current flow.
