>>11083246The idea goes at the heart of our general assumptions about everyday phenomena. In our everyday life, we assume "essences" of phenomanas. That is to say, we assume something discrete exist in nature. Whether that is our "souls" or the essences of objects. Mindfulness meditation simply breaks down those assumptions by pure observation/analyzing what is happening to our thoughts/mind.
How this is arrived while meditating is through mundane experience. For example, when you're meditating, you feel leg cramp (perhaps poor sitting posture) but when moment later you start thinking about the movie you watched last night, or maybe the food you ate, or you start remembering the last time you tried doing meditation, and so on. These moments of the mind last a brief period and you move on one thing after another. Sometimes you try clinging on harder for painful events, sometimes to joyful events, but nevertheless, it all moves forward. What this shows is our brain constantly generates thoughts with very little regard. The Buddhists call this "the monkey mind" as the mind just chases one thing after another endlessly. The part about the "ego death" is when you examine what really is "you" that you normally identify with. Is it your emotions or the feelings or the memories and so on. These things are merely the brain just automating stuff. Maybe you're saying its just the "clinger" who clings to these memories/feelings/experiences/etc. But then again, as these events come up and fade away without regard, the "clinger" is merely the illusion with regards to how hard some emotions/memories/experiences/etc are held and there's no real "clinger" other than a nominal designation.
Deeper/more you meditate, the more you begin to get a grasp of phenomena around you, all of it. Not just your own "selfhood" but also self hood of objects, events, identities of all sorts, and so on. This is the basic understanding of anatta(no-self) from the Buddhist. More insight are to had.