As its name implies, safe mode will basically see Tumblr attempt to filter out content that might not be safe for work. According to Tumblr, “Safe Mode filters sensitive content in your dashboard and your search results. Maybe you’re happy to see sensitive content when you’re scrolling through Tumblr, maybe you’re not. Safe Mode puts that choice in your hands.”
It is an opt-in feature meaning that if you don’t do anything right now, by default the feature is disabled meaning that your current Tumblr feed will not be changed. Users who want to turn it on will have to go into their settings menu to enable it, so even if you are finding out about this now, your experience will not be affected by it.
The feature is expected to be rolling out to all Tumblr users in the next few days, so if you don’t see it yet not to worry as the settings will eventually find its way to you.