When something menaces you, it puts you in danger. And something menacing—like a menacing stare, or a menacing voice—seems scary, threatening, and likely to attack you or destroy things.
A menacing dog looks dangerous and angry, like it might attack you.
As you can see, "menace" is often a very serious word for very scary things. But we can use this word more lightly. We can call someone a menace if they're just slightly annoying. And we can call something a menace if it's just a little troublesome. Take Dennis the Menace, for example! He's a cute, pesky little character who annoys his neighbor and makes a lot of messes.