Visakha is the name of a month of the Indian lunar calendar, and "puja" means "religious service." So, "Vesak Puja" can be translated "the religious service for the month of Visakha." In English, sometimes it is called "Buddha Day." Vesak is held on the first full moon day of Vesakha. There are diverse lunar calendars in Asia that number the months differently, but the month during which Vesak is observed usually coincides with May.
Most Mahayana Buddhists observe these three events of the Buddha's life at three different times of year. However, most of the time the Mahayana celebration of the Buddha's Birthday coincides with Vesak. Exceptions: In Japan, Buddha's Birthday is observed every year on April 8, by the Gregorian calendar instead of a lunar calendar. The Tibetan Buddhist equivalent of Vesak Puja is called Saga Dawa Duchen and usually falls a month later, in June.
For Theravada Buddhists, Vesak is a major Uposatha day to be marked by rededication to the dharma and the Eightfold Path. Monks and nuns meditate and chant the ancient rules of their orders. Laypeople bring flowers and offerings to the temples, where they may also meditate and listen to talks. In the evenings, often there will be solemn candlelight processions.
Of course, in some places the religious observances are accompanied by more gala, and more secular, celebrating -- parties, parades, festivals. Temples and city streets may be decorated with countless lanterns.
Washing the Baby Buddha
According to Buddhist legend, when the Buddha was born he stood straight, took seven steps, and declared "I alone am the World-Honored One." And he pointed up with one hand and down with the other, to indicate he would unite heaven and earth. I am told the seven steps represent seven directions -- north, south, east, west, up, down, and here. Mahayana Buddhists interpret "I alone am the World-Honored One" in a way that "I" represents all sentient beings throughout space and time -- everyone, in other words.
The ritual of "washing the baby Buddha" commemorates this moment. This is the single most common ritual, seen throughout Asia and in many different schools. A small standing figure of the baby Buddha, with the right hand pointing up and the left hand pointing down, is placed on an elevated stand within a basin on an altar. People approach the altar reverently, fill a ladle with water or tea, and pour it over the figure to "wash" the baby.