http://en.wikipedia.org/wiki/Miracles_of_Gautama_Buddha#The_Day_of_Miracles
The first full moon of the year is celebrated in the Vajrayana tradition as the Day
of Miracles, or Chotrul
Duchen in Tibetan, to commemorate the
final day of the 15 days of miraculous display by the Buddha. He
performed the miracles during this time to overpower the six
teachers of non-Buddhist views, called Tirthikas, who challenged him.
When the Buddha first received the challenge, he moved to another
kingdom of India[where?] and
he continued to avoid the teachers until he had visited all the
kingdoms. Finally, he had the kings of these lands and their
retinues accompany him to the final kingdom[where?].
There, at an arranged field, he allegedly displayed his miraculous
powers for 15 days to increase the devotion and merit of future
disciples. Through these acts, which are observed annually by the
prayer festival of the Gelugpa Monlam
Chenmo, the Buddha defeated the teachers.
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The clean water
Gautama Buddha asked his disciple Ananda to
get him some drinking water from a well. Ananda, however,
repeatedly told the Buddha that the well was filled with grass and
chaff, and thus not drinkable. Despite this, the Buddha
continuously asked Ananda for the well's water; eventually, Ananda
went to the well. As Ananda walked to the well, the Buddha
allegedly expelled all the grass and chaff from the well which
resulted in the water becoming radiant and clean.
It is recounted as one of the Miracles of Buddha that Gautama
Buddha walked on water by levitating over a stream in order to
convert a brahmin to Buddhism.[2]
R.C. Amore recounts a miracle from the first chapter of
Mahavagga
(Book of the Discipline, IV) where the Buddha displayed his power
over nature. When an area was inundated by a flood, he commanded
the waters to stand back so that he could walk between them on dry
ground.[3]
The golden bridge
During the third week after The Buddha's
Enlightenment, the devas were unsure about whether
Siddhartha Gautama had truly attained enlightenment or not. As
proof of his enlightenment, The Buddha, using only his mind,
allegedly created a golden bridge in the air, and walked up and
down the bridge for an entire week.
Twin miracle
After the Buddha returned to his father's kingdom, uncertainty
still existed about whether Gautama Buddha was really enlightened
or not. In response, the Buddha allegedly displayed the
Yamaka-pātihāriya or the "Twin Miracle", called so because of its
simultaneous production of apparently contradictory phenomena; in
this case, fire and water.
The twin miracle entailed Gautama Buddha producing flames from
the upper part of his body and streams of water from the lower part
of his body, alternating this, and doing similarly between the left
and right sides of his body.
Afterwards, the Buddha took three giant steps, arriving in
Tavatimsa. There, he preached the Abhidharma to his mother who had been
reborn there as a Deva named Santussita.
Brahma
On one occasion, the Buddha allegedly flew into a Brahma's world, and explained to the
Brahma that all things are transient and temporary and devoid of
independent existence. After being persuaded by the Buddha's words,
the Brahma decided to follow The Buddha's Dharma.
The Brahma then requested a competition of powers between the
two of them. Whenever the Brahma hid himself, the Buddha ended up
pointing out where he was located. Then, the Buddha hid himself in
voidness and meditation but the Brahma could not spot him. The
Brahma's faith in the Buddha was increased.
http://en.wikipedia.org/wiki/Miracles_of_Gautama_Buddha#The_Day_of_Miracles
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Are the Buddha Miracle Days the same every year ? If yes, which
days are they according to lunar calendar ?