This is a hard one, because it is almost impossible to explain something that can only be felt.
Maybe I can explain it this way:
If you are familiar with Eckhart Tolle, you will have heard him use the term "stillness".
Of course, he is not talking about the lack of sound.
In fact, he is talking about the opposite.
Silence is the basis of everything. Sounds may appear in stillness, but when the source of the sound disappears, so does sound itself, and only the basis remains.
It is like the cloth of a painting, the movie screen on which images appear.
This silence is the same as the silence of the soul. Your soul is always there. It never disappears, it is always there. Yet, because just like silence is shapeless and formless, so is the soul.
Silence is not the lack of sound, it is the basis in which the world of sound appears. Yet it is impossible to describe silence. It is there, but you can't describe what silence actually is.
The soul is no different. It is always there, it is the basis in which your world appears. Without the soul, there is no world.
At the end of a breath, when you stop exhaling and before you inhale again, this silence of the soul, this stillness, can be felt most powerful, especially at the end of a relaxing meditation session.
A good way of feeling it would be to try this little experiment. Very early in the morning, or very late in the evening, when all sounds outside have died out, sit in your room, preferrably with all noise makers turned off, like electronic hums from your fridge, your pc or whatever may make a sound.
In this extreme silence, you might notice a small hum in your ears. Even when your ears have never been damaged by any loud sounds, this hum is there, as your blood is forced through your hearing organ.
When you have done this excercise a few times, you will associate this hum in your ears with silence. And you will start to notice that you can hear that same hum even when in a noisy world. And if all goes well, you should immediately get that feeling of peace, of quiet silence inside your chest and stomach.
Every time your breath ends, and before you start your next, listen for this silence. And hopefully you will understand what they meant with that too from that moment on
