“I was introduced to him by a mutual friend.”
One of your friends knows a famous singer. Your friend invited you to a party, and the singer was there. Your friend introduced you to him. Now you're telling your sister about meeting the singer. She asks how you met him, and this is how you explain.
I was introduced to him by a mutual friend.
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When you know two people, and you want those people to meet each other, you "introduce them to" each other.
When someone introduces you to someone, you can say "I was introduced to ___ by ___":
I was introduced to the author by a friend of mine.
You name the person you met with "to" and the person who introduced you with "by".
A "mutual friend" is someone who knows both you and the person you're talking about.
You often use the phrase "a mutual friend" when you're explaining how you met someone:
We met through a mutual friend.
This example means that a friend who knew you and the other person introduced you to each other.