The umpire should make a "safe" signal any time there's a play where players and spectators might wonder whether or not a runner is out.
Here are some examples:
A fly ball is fielded immediately after hitting the ground (not caught in flight, but it was close), the umprie should say "no catch" while making the safe signal.
The defense attempts to tag any base runner, but the runner is safe because they reached the base before being tagged or the tag was missed.
The defense attempts to make a force out, but the runner touched the base before the fielder tags the base. If the runner was safe because the defender pulled their foot off the base before catching the ball, the umpire signals safe then makes a side sweeping motion with their hands to indicate the player pulled their foot.
If the defense makes an appeal claiming that a runner missed a base, or that they left a base too early on a caught fly ball, but the umpire judged that they did touch the base or did make a proper tag up, they would acknowledge but decline the appeal by signaling and saying "safe"
Keep in mind that a player can be safe, then become out, but they cannot be out then become safe. Once a player is out, that's it, they have to leave the field and they're out. But if a player is safe, then later is tagged or put out, they can be out.
So as an umpire, once you call a player out, you can't really change it. That runner's time on the bases is over. If you call a runner out and then overturn your call, you're going to have a lot of pissed off players. but if a runner is safe then there's another play that puts him out, its perfectly valid to call him safe, then out on the follow up effort.