One reason why I think Emptiness is so hard to understand, other than because of obscurations from past lives, is because it's always explained with a scholarly vocabulary. Although what I know about Dharma is like a drop of water in an ocean, I will try here to explain Emptiness for the benefit of all mother beings without jargon.
Nothing Has Self-Nature
Nothing exists independently. Nothing is permanent. Everything exists interdependently. Everything is impermanent.
Existing independently and permanently would mean the existence of a permanent self that exists by itself and does not change. This doesn't only include what you call your "I" as in "this is myself" or "I am Fred." This includes every speck of matter down to the atomic level, to the smallest particles. Nothing exists independently nor permanently. Therefore, nothing at all, down to the atoms, has self-nature.
I believe this is where folks get tripped up. Your mind wants to believe SOMETHING has to exist with self-nature. The fact is that, through analyzing yourself, others, and objects, you will not find anything at all, down to the atomic level, that exists with self-nature.
You have to understand that nothing has ever existed with self-nature. It is only a concept, a false one.
This is why you see so many debates among Buddhist schools. Only the highest school, the Madhyamaka Prisangikas, understand that nothing at all has self-nature. Other schools can't seem to wrap their heads around this. They try to shoot down the Madhyamaka Prisangika view, saying that if nothing has self-nature, then the very words they use to describe their system couldn't be possible.
So what about "I", "Fred", or "Self?" These are merely labels projected by the mind onto the mind and body combination that make up "I" or "Fred" or "Self." This is how your "I" truly exists, as a mere label projected by your mind onto your mind and body combination.
The way you normally think "I", "Fred," or "Self" exists is by believing your "I" is somehow ON your mind and body combination.
For example, when you were born, your parents named you "Fred." They slapped the label "Fred" onto your mind and body combination. This is correct.
However, when you believe "Fred" exists as somehow part of your mind and body combination, this is incorrect.
If you analyze your mind and body you will see that it is not made up of anything that has self-nature. Your body is something like 70% water, sunlight, the food you eat, the air you breathe, etc. This is the interdependent nature of your body.
Furthermore, water, sunlight, food, and air also exist without self-nature. Water, for example, is made up of two parts hydrogen and one part oxygen.
And so on. Hydrogen doesn't have self-nature either. Neither does oxygen.
The atoms that form these molecules and stuff don't have any self nature.
That's because nothing at all has self-nature. Nothing exists independently and nothing is permanent. Instead, everything is interdependent and everything is impermanent. And the labels project onto these various combinations of Self, Other, and Objects are merely labels. That's because all of these interdependent things require labels to designate them by name.
Okay, so, Emptiness means empty of Self-Nature.
This can all be understood in a more organized way called Dependent Arising. There are 3 Levels of Dependent Arising.
Level 1 - Everything exists because of interdependent causes and conditions. For example, a tree is made up of sunlight, soil, oxygen. Then we slap the label "tree" onto it to designate it as a tree.
Level 2 - Everything exists because of its interdependent parts. A tree has branches, a trunk, leaves. None of these parts are a tree. But they all make up a merely labeled "tree." Your mind projects the label "tree" onto a tree, which is made up of a bunch of non-tree parts. And, all the parts of the tree can be examined likewise, down to the atoms. The whole "tree" exists through a combination of interdependent parts that have no Self-Nature.
Level 3 - A "tree" can also only come into existence with the label "tree". If you're not standing there, looking at the "tree," then the "tree" doesn't exist because it requires your mind to project the label "tree" onto it. This is because, remember, a "tree" is only the name given to label this combination of interdependent parts.
So, how do we actually use this understanding of Emptiness of Self-Nature to lessen and eventually destroy all ignorance and afflictions within our mental continuum?
You must examine your self, others, and objects (like a tree) and analyze them based on these 3 Levels of Dependent Arising. If you do this just with mindfulness in everyday life and meditation, you will begin to cut at the root of ignorance. You will begin to see reality as it truly is.
Also, you must identify the UNTRUE Self-Nature of self, others, and objects and cast it aside. For example, you must analyze self, others, and objects to see where there SEEMS to be Self-Nature and cast this aside. This is called the object to be refuted--"refuted" means: prove (a statement or theory) to be wrong or false; disprove. Once you have refuted the existence of Self-Nature, you can begin to see the Emptiness of Self-Nature of self, others, and objects.
The first way to do this in meditation is by identifying the object to be refuted within your body and mind combination. This might arise as a feeling in your chest or in your head when you're angry or jealous or feeling any affliction. This is the very root of ignorance that needs to be sliced.
Once you've identified the object to be refuted, cast it aside, and try to focus only on its non-existence, because Self-Nature doesn't exist at all. Rest in this Emptiness with single-pointed concentration and alternate between analyzing the Emptiness of Self-Nature using such reasoning as above and switching back and forth between the two. When understanding of Emptiness arises, focus on it single-pointedly. When that understanding weakens, switch back to analyzing Emptiness.
Emptiness only means Empty of Self-Nature. Therefore, you begin to touch reality when you identify the object to be refuted and rest in Emptiness of Self-Nature.
Emptiness simply refutes Self-Nature. So, while your experience of reality is a non-conceptual one, it does not mean just resting your mind in no concepts. It must be specifically resting your mind in the absence of the concept of Self-Nature.
Because this is how the ignorance of Self-Nature works. It was never there in the first place. It is merely projected by your mind onto reality. It's like your mind is adding something to reality that was never there in the first place.
So, in order to touch reality, you must refute your mind's projections of Self-Nature onto reality. Then you will experience reality.
With this first meditation you will begin letting go of the wrong idea of Self.
If you can imagine, it's almost like there are two selves, the wrong self and the right self. The wrong self is the self you project onto your body and mind combination that seems have Self-Nature, independent and permanent. The right self is the mere label of "I" used to designate your interdependent and impermanent collection of body and mind.
How do you examine the body and mind, though, to find the object to be refuted?
First take a look at your body. Scan it. See that every inch of your body is made up of interdependent, impermanent stuff. You will not find any independent, permanent stuff anywhere on your body or in your body. Plus, think about how you say "my body" as if you are the owner of your body. This means "you" can't be on your body.
Now think about your mind. If you're saying "my mind" then that assumes "you" own your mind. Therefore, "you" can't be anywhere on your mind.
Now examine your body and mind together. An independent, permanent self can't exist between these two things. That would be absurd.
Now examine now how your "self" can't exist somewhere outside your body and mind combination. That would be absurd.
What does examining your body, your mind, and your body and mind combination reveal? That there's no Self-Nature to be found anywhere.
This lack of Self-Nature is Emptiness of Self-Nature.
Now rest in this knowing of Emptiness. Use this reasoning in analytical meditation, then once this understanding has risen, focus single-pointedly on this knowing. Interchange between analytical and single-pointed meditation like this.
The next meditation is to take this same reasoning and use it toward others and objects.
At first you will see only a generic image of Emptiness, then you will begin to cut through that and touch actual reality. Over time, your obscurations and afflictions will lessen. Your ignorance will lessen. Your self-grasping will lessen.
You can begin doing this now, but to truly touch reality you must train your mind in single-pointed meditation known as Calm Abiding. There are nine levels of Calm Abiding to achieve. However, I believe that if you can achieve Jhana through the Theravada tradition, then use that powerful, laser-like focus to analyze Emptiness of Self-Nature the way described above, then this is comparable.
Anyway, I'm just trying to help and I hope this does help you deepen your understanding of Emptiness. I'm certainly not trying to be a know-it-all. Writing this out helps me too. Please forgive any errors. I'll try to correct it all.
May the merit of this post be dedicated to the enlightenment of all mother beings.