Purnima refers to full moon night. Sharad Purnima is celebrated on the full moon night of Ashvin month (September to October) according to lunisolar Hindu calender. It is also known as Kumara Purnima or Kaumudi Purnima. It marks the end of monsoon season.
The Moon is said to be closest to the Earth on Sharad Purnima and the moon rays are said to have healing powers on Sharad Purnima. People prepare sweet dishes of milk, especially Rice Kheer and they keep it under the moonlight on Sharad Purnima night. The moon rays falling on rice kheer are said to enrich with healing properties. According to experimental research, the Rice Kheer should be stored in silver container which enriches its properties more as Silver has more healing power. Spicy food should be avoided.
Major question is why only Rice Kheer? There is presence of lactic acid or lactate in milk and in presence of rays, it produce more energy. And as there is presence of starch in rice, this process becomes easier. That is why Vedic sages suggested to keep the Rice kheer in moonlight on Sharad Purnima.