When practicing meditation (samatha and vipassana) intensely it feels like the sense of self is disintegrating and breaking apart. What causes that?
The Pali suttas teach self-identity is born from craving. For example:
The craving that makes for further becoming — accompanied by passion & delight, relishing now here & now there — i.e., craving for sensual pleasure, craving for becoming, craving for non-becoming: This, friend Visakha, is the origination of self-identification described by the Blessed One. MN 44
He assumes form to be a self. That assumption is a fabrication. Now what is the cause, what is the origination, what is the birth, what is the coming-into-existence of that fabrication? To an uninstructed, run-of-the-mill person, touched by that which is felt born of contact with ignorance, craving arises. That fabrication is born of that. SN 22.81
And what may be said to be subject to birth? Spouses & children are subject to birth. Men & women slaves... goats & sheep... fowl & pigs... elephants, cattle, horses & mares... gold & silver are subject to birth. Subject to birth are these acquisitions, and one who is tied to them, infatuated with them, who has totally fallen for them, being subject to birth, seeks what is likewise subject to birth. MN 26
From when you were very young, your mind attached to things due to both craving & fear. For example, as a baby, your body was hungry and you attached to your mother, who was the source of food. Or when you were lonely & frightened, you craved your mother's attention. Since your children, your life has probably continued like this. While you may not crave your mother for food & comfort, you probably have sought pleasures & attention from other things, so to escape the instinctual fear of being alone, bored & restlessness. From these objects the mind craves & attaches to, a sense of self-identity is born, such as: "My mother, my toys, my food, my friends, my girlfriend, my boyfriend, my husband, my wife, my profession, my sport, my favourite pop star, my favourite movie, etc".
Meditation is similar to being alone. Because the sense of self-identity is built upon external attachments, the sense of self-identity can reduce &/or break apart in meditation. What remains is the original fear the mind has been escaping since it was born into the world.
If your mind is naturally strong, you endure this fear until it passes. Even the Buddha did this, as described below:
So when fear & terror came to me while I was walking back & forth, I would not stand or sit or lie down. I would keep walking back & forth until I had subdued that fear & terror. When fear & terror came to me while I was standing, I would not walk or sit or lie down. I would keep standing until I had subdued that fear & terror. When fear & terror came to me while I was sitting, I would not lie down or stand up or walk. I would keep sitting until I had subdued that fear & terror. When fear & terror came to me while I was lying down, I would not sit up or stand or walk. I would keep lying down until I had subdued that fear & terror. MN 4
However, there are meditators unable to endure this fear. For example, i listened to a Western monk of 30 years who has given up on even trying to overcome this fear. He spends most of his time as a monk talking & teaching.
This lecture has a good introduction about what the 'self' is: Anattā and Rebirth by Buddhadāsa Bhikkhu
It's caused by the sense of self disintegrating and breaking apart. That's kind of the whole point. What you think of as you, the thing you identify with your name, is actually a fiction. It's just a concept, an agreed upon convention. It's convenient...I mean, having a name makes it a lot easier for your boss to pay you at the end of week...but this you who you take to be you keeps you from seeing who you really are.
Buddhist practice is many things, but chiefly it is a process of disentangling our mistaken identities. It's about ceasing to identify with this flesh, this mind, these habits, these loves, and these hates and instead seeing ourselves as not body, not mind, no habits, and something that is beyond love and hate. Undertaking this process can be painful. Nothing characterizes our smaller selves more than its desperate scrambling for continued existence. The more you sit, the more insight that awakens, the more it will claw and scratch. If you are going to practice the great way, be prepared to struggle. Be prepared to be wounded.
"When you realize what the real is, you will see that we pass from one husk to another like travelers stopping for a night's lodging. But if you do not realize it yet, I earnestly advise you not to rush about wildly. When earth, water, fire, and air suddenly separate, you will be like a crab struggling in boiling water with its seven or eight arms and legs. When that happens, don't say I didn't warn you."
From Case 35 of the Mumonkan