Similarly, are arms passive in golf swing?
Passive arms simply means that you're not expending any energy with the arms in the downswing. It doesn't mean that your arms are limp noodles. It just means you're not trying to do anything with them. You're working to conserve energy, not accelerate.
In this way, what does staying connected mean in the golf swing?
Staying connected is a common phrase you'll hear in golf, but what does it really mean? It assumes the premise that when the arms and body are moving together, the overall timing of the swing and path of the golf club will be improve and provide better and consistent ball striking.
You should pull the butt of the club toward the ball. Remember, this pulling down is done by the left arm. By pulling down with the left arm and keeping that arm straight you automatically bring the right arm into the proper hitting position: the elbow is leading and the upper arm comes in close to the body.