I was always mystified by this phrase from girls/women for a long time. What the hell were they talking about? Do they walk around feeling in danger all the time? And safe from what exactly? We have very little danger in society! As a man, I could never relate to this on their level.

Being "Safe" is really about two things - Safe physically and Safe emotionally. Women have strong instinctual needs for both. I won't bore this thread with topic of why... but my guess would be it's evolutionary. Women are vulnerable as hell, prone to more mental instability and physically weaker. The fact that society protects them doesn't quite change the biological instincts.

Safe Physically - Though not the only reason, this is a big deal in why women are attracted to tall, muscular, and dominant men. Such a man is communicating to her that he can provide safety from physical threats. This carries over to her eventual children, as well.

You can find guys yelling about this angrily on the internet. Women will often admit to feeling safe with taller/bigger guys. A lot of angry dudes try to logic their way out of this by bringing up arguments about how society is pretty safe or they could just carry a gun and shoot the bigger guy or a million other things. It doesn't matter, it's an emotional reaction to men that are physically and/or socially dominant.

Safe Emotionally - I think this one could be even more important. We talk about it all the time here. Women are more volatile emotionally. They're more prone to negative emotions and thoughts. They need emotional security and safety. Again we come back to TRP beliefs... About men being emotionally stoic, maintaining frame, being calm in the face of pressure, not acting out on emotions, etc. All of this communicates to her that you withstand anything and handle yourself in any situation. It makes her comfortable and secure, because if something bad happens, you're there to take care of shit. Above all, you can handle her. And if she trusts you to do that then she can really be at ease.

So What - I know guys, this probably doesn't help with bar hookups and flings. But as a guy who enjoys my LTRs, I find this to be pivotal for my relationships. I believe that this feeling of safety makes for more uninhibited sex, a submissive girlfriend, and cuts down on bad behavior from her.

TL;DR: When the leader makes his people feel safe, they are comfortable and behave better.