To stand down means to stop fighting or competing, especially when you were ready to fight or compete.
Standing down can be a good thing because it can mean that people are choosing peace instead of fighting.
Examples:
The soldiers will stand down and go home.
I will stand down and let you win.
The teams decided to stand down and not play the game.
The cat and dog were going to fight, but then they decided to stand down and be friends instead.
The superhero stood down and decided not to fight the bad guy.
The boss told everyone to stand down and stop arguing.