In baseball, a baserunner is safe when he reaches a base without being put out by various ways.
While a runner is touching a base, he is usually not in jeopardy of being put out, and is thus "safe" from fielders' actions, such as tags.
For emphasis, an umpire may fully cross and extend his arms several times to indicate safe.
If a close play occurs that may have appeared to be a putout, the umpire will also call a reason for the safe call, such as "he dropped the ball" or "he missed the tag".
Calling safe is a subjective decision which is better made using the sounds of the runner hitting the bag and the fielder catching the ball, rather than by sight.