This quotation is a part of a poem. There are two kinds of sound, heard and unheard (aahat and anaahat in Sanskrit). The first kind is the one that the ears perceive, the second is what we hear when we completely turn off the senses of perception. The unheard sound is a realization, not perception. And that is the sound of silence. In some contexts silence can be more eloquent than words.
It may all seem a contradiction in terms. After all silence is defined as absence of sound. But words have an inherent limitation in conveying ideas. A word is merely a symbol for the reality behind it and the symbol, by very definition, is not the reality. Whenever we define something in negative terms, it only means that we cannot describe its essence in words. Silence is that unheard sound which can only be realized.
In order to perceive anything with our senses we need a background of contrast. We see stars or other objects on the background of the sky that is total emptiness. Similarly we hear something on the background of silence, which is also emptiness. Emptiness is absolute, it cannot be described in terms of anything else except in negative terms. Emptiness actually defines all objects. A vessel would not be a vessel without the emptiness. Taking a more esoteric view there would not be any life without it; we could not breathe if there were no emptiness in the lungs.
In a real sense emptiness is the background for everything that exists. When we say that something is empty we simply mean that it does not contain anything that we can perceive. The range of human perception is limited and if we cannot perceive, it does not mean that nothing exists. In the case of sound we know that it is simply a form of vibration. (In fact every sense perception results from some form of vibration.) These vibrations cover all frequencies but we cannot hear anything above or below a very limited range. Still the vibrations do exist and medical science has put some of these to practical use for diagnostics and treatment. So what we call silence is not really absence of sound but absence of auditory perception.
The absence of perception can also be brought about deliberately through meditation for example, when one literally shuts off all the senses of perception. It is believed that ancient sages could hear the inner vibrations in this state, which was the sound of the Self. Since it is heard in the state of bliss, it is sweeter than any other sound. The sound was that of the word Om that is synonymous with the Ultimate Reality (or God). This word has three components for its sound those of the letters A, O, and M. Because of this origin it is the most sacred sound in Vedanta.
When the mind is completely devoid of thought and there is no sense perception from outside, one hears the unheard sound (anaahat naad in Sanskrit) the vibration of the pure Self. This state of mind can also come about in other situations. When a person is intensely watching a serene sunrise or sunset on a lonely beach, he becomes one with the nature. Even though there might be other sounds around, they practically do not exist for him and he hears only the silence within.
In Vedanta and Buddhism the term used for this concept is shunyataa. There is no exact equivalent word for it in English and emptiness or void does not really convey its real meaning. Shunyataa is the Ultimate Reality from which everything in the universe (matter, space, time) evolves; it is the Universal consciousness that also contains the cosmic energy. The term also includes silence that we are talking of. This concept of emptiness is in fact is basic to everything. The atom that is the building block for all matter is more than ninety percent empty.