I never understood silence or emptiness in Buddhism and how is experiencing them beneficial?.Is it a way for experiencing the arising of experience ?
Silence in Buddhism refers to Citta Visuddhi. This means the purification of the mind, or quietening of the mind. It doesn't mean no sound. This is when the mind attains highly concentrated states called the Jhanas. When the mind is in these states, your defilements are silenced or subdued. This is a good base for the development of insight meditation.
'Emptiness' is a nature of all realities. It doesn't mean empty in the literal sense. It means being empty of a self or a soul or an entity. This is a truth one realizes with insight meditation. It is one of the Three characteristics of all condition phenomena. Realizing them lead to enlightenment.
In contemporary physics we accept the idea that everything is empty, but since our senses and minds are full of "things" we have a difficult time reconciling what we know with what we experience. Buddha teaches that all things are essentially empty, but mostly it is in the sense that all things are empty of a self-nature, that all things are made up on non-thing elements. Thus the form of things, what we experience, is synonymous with the emptiness of things (which we may or may not know we also experience).
There are several Pali Canon suttas that convey Buddha's teaching about emptiness, and the Theravada and Mahayana schools interpret differently, this has been a past topic on Buddhism Stack Exchange (see Related posts in the lower right)
Why emptiness is of importance goes back to the idea of the Four Noble Truths. We suffer, there is a cause of suffering, removing the cause of suffering removes the suffering. There is a Path that does this. The liberation of the mind infused with Emptiness is the removing of the cause of suffering. It is the natural, liberated state of the mind.
In the high spiritual stages the mind becomes naturally more quiet, because there is no longer identification with the self/ego which means there is no longer identification with the thoughts, emotions and feelings. Also there are some temporary states of mind that can a meditator experience in the path that completely silent(absence of thoughts). Also the the momentum of the thoughts can be slowed down and there can be big gaps between the thoughts.
The important thing is what is a person's relationships with the thoughts. The thoughts, emotions and feelings continues to occur but If there is no identification with them they would not be serious for a person anymore and also they would naturally be less then before. As a result a person would have more peace, tranquility and happiness.
As for the emptiness, this answer is related to the subject: https://buddhism.stackexchange.com/a/31632/700
A person can experience emptiness in different degrees many-many times and as the person experiences the emptiness more and more with higher awareness s/he would lose his/her attachment to self and would start to see things as they are(without judging and being attached to things) The nature of everything is being empty of a self.