"I'm on my way". Could you explain me what exactly this phrase mean?
Give me some examples please.

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i'm on my way means that I have arranged to meet you and have already started on my journey to you.

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The full sentence is "I'm on my way to you" or "I'm on my way there".

It means the person is travelling to you and has already started their journey.

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Hi, vivaldo. When you say "I'm on my way" it means that you are going to the person.

I got your message saying you needed my help. I'm on my way.
Just be patient, I'm on my way."
Don't worry I'm on my way."

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I have already started to go to the place we just talked about or I am telling you about now,

"Hey John. Where are you? Are you coming to the mall?" 
"I'm on my way"

"Have you left the house yet? We don't have much time"   --- "Don't worry I'm on y way and I'll be there soon"

"I'm on the bus to the airport. I'm on my way to France!"

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This sentence means that you are going somewhere and you are telling someone you are coming. So you would say this when you're about to travel to a destination. 
examples: 
1. I'm on my way to your house. 
2. She's on her way. 
3. Ted is leaving the restaurant now, he's now on his way to the grocery store.