に (target)
to (the person on the receiving end)
Person + に + verb
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に also marks the person an action is aimed at: 友達に手紙を書きます, "write a letter to a friend"; 母に電話します, "call my mother"; 先生に聞きます, "ask the teacher".
Think of it as the target of an arrow: the action goes from you to them. Verbs of giving, sending, showing, teaching and telling all work this way: 弟に本をあげました, "I gave my little brother a book".
会う takes に too: 駅で田中さんに会いました, "I ran into Mr Tanaka at the station". と is also possible, since meeting is mutual, but に is the everyday choice. What 会う never takes is を.
Examples
母に電話します。
I'll call my mother.
友達に手紙を書きました。
I wrote a letter to a friend.
分からない時は先生に聞いてください。
If you don't understand, ask the teacher.
弟に本をあげました。
I gave my little brother a book.
昨日、駅で田中さんに会いました。
I ran into Mr Tanaka at the station yesterday.