As I know, Lord Hanuman's parents were Anjana (mother) and Kesari (father). Then why is Lord Hanuman also known as "Pavan putra Hanuman" (Son of lord Pavan)?
It was because, Vayu god had impregnated Anjana through his mind. Hence, Hanuman, although was born from Anjana and Kesari, is also known as Pavan-putra (son of wind):
मनसा अस्मि गतो यत् त्वाम् परिष्वज्य यशस्विनि |
वीर्यवान् बुद्धि संपन्नः पुत्रः तव भविष्यति || [VRM - 4.66.18]
By which reason I embraced you and impregnate myself within you through my mind, by that reason you are impregnated in a super sensory manner, thereby you will beget a valiant son endowed with intellect
The 66th chapter of Kishkinda Kanda in Valmiki Ramayan describes the whole story.
स त्वम् केसरिणः पुत्रः क्षेत्रजो भीम विक्रमः
मारुतस्य औरसः पुत्रः तेजसा च अपि तत् समः
त्वम् हि वायु सुतो वत्स प्लवने च अपि तत् समः [VRM - 4.66.29,30]
Such as you are, you are Kesari's son through his wife, oh, frightful pugilist, and you are the lineal son of Air-god, and even by your gusting you are selfsame to Air-god, and even by your flying also you are his selfsame to Air-god, in all respects
When Anjana ( Hanuman's mother) was worshipping Shiva, the King Dasharatha of Ayodhya was also performing the ritual of Putrakama yagna in order to have children. As a result, he received some sacred pudding (payasam) to be shared by his three wives, whic lead to birth of Rama, Lakshmana, Bharata, and Shatrughna. By divine ordinance, a kite snatched a fragment of that pudding and dropped it while flying over the forest where Anjana was engaged in worship. Vayu, the Hindu deity of the wind, delivered the falling pudding to the outstretched hands of Anjana, who consumed it. Hanuman was born to her as a result. And hence Hanuman is also called "pawan putra' (Son of Wind)
Hanuman is called pavana putra meaning son of wind because he was born with the blessing of the wind, he had the courage, strength and passion of the raging wind, yet the sensitivity and awareness of the breeze. Hence he is known as Vayuputra, the son of the Air. read hanuman chalisa in english to get power from Hanuman.
Once, God Shiva and Parvati went to Venkatachala hill where they saw 2 romantic monkeys. God Shiva took the form of a monkey and lovingly embraced Parvati. Unable to bear the radiant fruit, she gave it to Agni who too could not carry it. He gave the fruit to Vayu.
At that time, Anjana was performing great tapasya to obtain a son. Vayu carried God Shiva's fruit and put it in her hands. She ate the radiant fruit. She got worried when she conceived as she was pativrata (chaste). An akashvani told her that it was divine blessings and there was nothing to be worried about. God Hanuman was thus born to her [Ref: Essence of Parashara Samhita 6.21-41 translated by Dr Annadanam Sasthry].
Thus, God Hanuman is called Pavan-putra, Anjaneya and Kesari-nandan.
This also explains why God Hanuman is called God Shiva's son [Ref: Parashara Samhita 54.8 translated by Dr Annadanam Sasthry].
As per local folklore, Vayu handed over the fruit to Anjana at Anjani-Devi temple in Anegundi near present-day Hampi in Karnataka state, and God Hanuman was born at Anjaneri near Nashik in Maharashtra state.