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Edit: the following is based on my experience, I can't make claims about all meditation.

It takes a lot of practice to actually be able to do that. The distraction is the meditation - you need to learn notice it and bring your mind back. The drowsiness is the meditation - you need to learn to notice it and raise your energy.

And as you learn to calm your brain without falling asleep, deeper and deeper repressed and ignored thoughts and feeling will come to the surface, because as you're gradually calming all the parts of your mind you are also calming the parts that are repressing the other parts which are enraged and demand a seat at the table. And part of meditation is getting punched in the face by those parts that you have been repressing, until you have faced them, dealt with them, accepted them and integrated them. (Although part of it is also learning when you need to ignore them and not try to "face" or "deal" with them.)