In Buddhist practice you say certain mantras 10,000 100,000 or 1,000,000 times.
It is why you see Buddhists with "prayer beads". The string of beads is a certain number, and you move your fingers to the next bead after each uttering. (they have little silver dangles on them to count multiple iterations through the string.)

Now, a non-new-agey statement to make is that the brain rewires itself based on exposure.
Everything that goes into your brain strengthens or weakens connections (or makes entire new connections)
Thus, putting in good affirmations repeatedly will rewire your brain and how you experience the world.

Now, the new-agey stuff. This change not only changes you, but changes the world you experience.
Two different people, walk down the same street, one gets mugged all the time, the other never experiences a mugging. Luck? Not really. Once can be luck, but many times, there is something going on, some law of the universe happening. And the reality is these two people live in different universes.

It could be that one walks like she is a prey animal. She opens her purse for all to see. She just attracts ne'er do wells. The other person walks confidentially, doesn't appear to have anything worth the fight... or maybe she looks like everyone's mother. But these are the outwards signs of the inner world. Mantras change the inner world.

And

They fell, together with chakras, energy, vibrations, and everything...

It is interesting that you used all of these words.
All of these phenomena are very real. Some day we will have instruments to measure and see them.

They are only controversial because everyone cannot see them, and also the people that talk about them see really unhinged.

The problem with your stance is that you are very likely to run smack into these things. If you continue on with meditation, you will start to see, feel or sense them. (or maybe not, some people never do) Then these things become very real. More real than what you considered "real life".

I am glad you are learning to meditate. Quieting the mind is very important to thinking.
Your thoughts will be clearer and more effective.