Another word for "weapons" is "arms," and to arm people is to give them weapons or powers. The opposite of arming people is disarming them: that's taking away their weapons or powers. In the image below, the guy in the red suit is disarming the guy in the white uniform.
That's a very literal kind of disarming. But most of the time, we use the word "disarming" more figuratively.
Imagine you're in some situation where, normally, you'd feel tense or nervous, or you feel like you have to defend yourself or be on your best behavior. But then, imagine that you meet someone who's so nice, so kind, or so charming that suddenly you feel very relaxed around that person. That person has disarmed you. With their disarming voice, their disarming smile, or their disarming gentleness or friendliness, this person has made you feel as if you don't need to protect yourself, or feel upset, or use any kind of weapon or power. You feel friendly and trusting toward this person. They've made you feel calm and safe.
To sum that up, disarming people are soothing and charming, and they put other people at ease.
If it's your first day at a new school, or your first day at a new job, you probably feel nervous. But if your teacher or your boss gives you a disarming smile and a disarming welcome, then you'll feel more relaxed.
If you're about to compete against a new team, you might feel tense or even defensive, ready to show this other team how tough and strong you are. But if they give you a disarming smile, a disarming handshake, or a disarming "Good luck out there!"—then you'll relax. You'll feel less eager to show your strength, and more eager to just play, have fun, and do your best.
If you're about to be interviewed on television, you might feel scared and stiff, afraid of saying the wrong thing or sounding stupid. But if your interviewer gives you a disarming smile, as if she's your friend instead of a stranger, then you can probably chill out and enjoy chatting with her.