This history is found in the Padma Purana, Srstikhanda, Chapter 17:

Once Lord Brahma came to know that a demon, Vajranash, was killing people. Lord Brahma chanted a mantra on a lotus flower and killed the demon. During this process, the parts of flower fell on three places which were later known as Jyestha, Madhya and Kanistha Pushkar.

Later accompanied by brahmanas and other devas, or demigods, Lord Brahma went to Puskar to perform a sacrifice. To perform his yajna peacefully without being attacked by the demons, he created the hills around the Pushkar. Ratnagiri in the south, Nilgiri in the north, Sanchoora in the west and Suryagiri in the east and positioned demigods there to protect the yajna performance. Such Yajna sacrifices are to be performed along with one’s wife, so when the arrangements for the sacrifice were complete, Lord Brahma sent Narada rsi, the sage among the devas, to bring Sarasvati, Lord Brahma’s consort. But Sarasvati was not ready to leave, so Narada returned to Puskar alone.

According to astrological calculations, the sacrifice had to begin at once, so Brahma asked Indra, the king of the heavenly planets, to provide him a suitable wife to assist in the sacrifice. Lord Indra chose a cowherd girl, but the sacrifice required that the girl be of the brahmana caste. So the devas purified the girl, or elevated her caste, by passing her through a cow (into the cow’s mouth and out the other end), because in Vedic culture cows are considered pure and of the same caste as the brahmanas. The girl then became known as Gayatri, “one who was pulled through a cow.” She married Brahma and performed the yajna. When Saraswati arrived and saw that Brahma had married without her permission, so she cursed Brahma saying that he would be worshiped in Pushkar only. Saraswati (Savitri) also cursed Indra to be easily defeated in battles, Lord Vishnu to suffer the separation from his wife as a human, the fire-god Agni who was offered the yajna to be all-devouring and the priests performing the yajna to be poor. Endowed by the powers of yajna, Gayatri however diluted Saraswati’s curse, blessing Pushkar to be the king of pilgrimages, Indra would always retain his heaven, Vishnu would be born as the human Rama and finally unite with his consort and the priests would become scholars and be venerated. Enraged Saraswati (Savitri) went and established a temple on top of Ratnagiri, the hill a little south of Pushkar. Today pilgrims to Pushkar can visit temples of both Sarasvati Devi and Gayatri Devi. Sarasvati Devi is also present in this world in the form of a river. Five branches of that river Sarasvati, Supapra, Candra, Kanaka, and Nanda flow in the Pushkar area, but at present they are invisible to ordinary eyes.

It is also said that Lord Varaha appeared at Varaha ghat here, and Lord Rama came and bathed here. The sage Parasara is said to have been born here. His descendants, called Parasara brahmanas, are still found in Pushkar and the surrounding area.

The Vedic scriptures tell us that Lord Brahma was born from a lotus flower sprouted from the navel of Lord Garbodakasayi Visnu. Because Brahma was not born in the ordinary way, he is known as atma-bhü, “the self-born.”

Brahma is called the creator of the universe and he creates by the power invested in him by Lord Visnu. In fact, the position of creator, which Brahma occupies, is a post to which Lord Visnu assigns a highly qualified living entity. Though Brahma is posted above all the other devas except Lord Siva and Lord Visnu, his main qualification is that he understands himself to be an eternal servant of the Supreme Lord. Pilgrims to Puskar, aware of Lord Brahma’s exaltedness, generally petition Brahma for material rewards, such as elevation to the heavenly planets. But people with a higher understanding know that such rewards cannot match the gift of pure devotion to the Supreme Lord, which Lord Brahma can also give.

The first verse of the Bhagavatam says that the Supreme Lord awakened transcendental knowledge within the heart of Brahma. After much penance, Brahma realized that the Absolute Truth is Lord Sri Krsna, of whom all living entities including him are eternal servants. Lord Brahma is also the head of one of the four Vaisnava Sampradayas, or disciplic lines of devotees of Visnu or Lord Krsna. Sri Caitanya Mahaprabhu, who is Krsna Himself, aligned Himself with the Brahma Sampradaya. The International Society for Krishna Consciousness, which descends from Lord Caitanya, is a part of the Brahma Sampradaya.

Mahabharata says- The holy place of Lord Vishnu, Pushkar-tirtha, renowned in the three worlds, is situated on this earth. Fortunate souls can enter that place. O son of the Kuru dynasty, at Pushkar billions of tirthas gather at sunrise and sunset. Simply taking bath at Pushkar destroys sin of both men and women, including the sin that caused their birth. As Madhusudana is the original God, so Pushkar is the original tirtha.

The Mahabharata says that while laying down a program for Maharaja Yudhishthara’s travel, “Maharaja after entering the Jungles of Sind and crossing the small rivers on the way should bathe in Pushkara”.

In the Mahabharata, while describing to Bhisma, the grandfather of the Pandavas, the glories of many tirthas, or holy places of pilgrimage, the sage Pulastya mentions Puskar Tirtha first. He says that Puskar is famous throughout the universe and anyone who goes there becomes as exalted as Lord Brahma. Among various blessings obtained by bathing at Pushkar: one may be elevated to the heavenly planets, even the planet of Lord Brahma.

Later when after Brahma had empowered Puskar to grant these extraordinary blessings, some of the devas, or demigods, complained to him that he had made it too easy for people to attain the heavenly planets. They feared that people would neglect their religious duties and the earth would be plagued with irreligion and its consequences. Lord Brahma conceded and proclaimed that from that time on, the boon of elevation to heaven by bathing at Puskar would be granted only during the last five days of the month of Karttika (October–November). Today tens of thousands of people visit Puskar during that period, and a great festival takes place.

As per Vaman Purana, Prahlada on his pilgrimage to holy places visited Pushkarayana.

The Ramayana mentions that Vishwamitra performed penance at Pushkar Lake for thousand years. Inspite of Brahma appearing before him and granting him the higher status of a rishi instead of a royal-sage (rajarishi), Vishwamitra continued his penance, but, the apsara, Menaka came to the lake to take a bath. Vishwamitra was enamored by her beauty and they decided to live together in pursuit of pleasure for ten years. Then, Vishwamitra realized that his main activity of penance was disturbed. He, therefore, took leave of Menaka and went away to the north to continue his meditation.

Srimad-Bhagavatam (12.12.61) states, “One who controls his mind, fasts at the holy places Puskar, Mathura, or Dvaraka, and studies this scripture will be freed from all fear.”

Once Lord Brahma, the empowered creator of the universe, desired to have a place on earth dedicated to him. So he threw three lotus petals toward the earth. When the petals landed, three holy lakes sprung up. Because the lakes were created from the flower (puñpa) thrown from Brahmä’s hand (kara), the area is known as Pushkar. The three lakes are known as Jyeñöha Pushkar (senior Pushkar), Madhya Pushkar (middle Pushkar) and Kaniñöha Pushkar (junior Pushkar) or Budha (old) Pushkar, as it is more commonly known today.

These three places are located within the radius of six miles.

1) Senior Pushkar- It is the place where hotels are located. It is considered the most holy, because the lotus fell here first.

2) Middle Pushkar- It is three kilometers down the road. It has a small hanuman temple and a 200 year old banyan tree.

3) New (junior) Pushkar- It is three kilometres further north. It has a small Krishna temple. Pushkar word may also be derived from word ‘Pushkarni’ which means ‘lake’.