May 23, 1844, is the beginning of the Bahá'í calendar. The Báb, the Forerunner of Bahá'u'lláh, Prophet-founder of the Bahá'í Faith, declared His Mission two hours and eleven minutes after sunset the evening of May 22, 1844. As the Bahá'í day begins at sunset, the holy day on which work and school is suspended is May 23.
At that time in history, many religious scholars were in some furor over the belief held by messianic movements within their faiths that centered around the early years of the 19th Century. Jews were looking for the Messiah. Christians were expecting the return of Christ. Moslems awaited the Qá'im; Buddhists believed the Fifth Buddha was coming to transform the world. Sects within every major religion were ardently preparing for Judgment Day.
Within Shí-ih Islam also there were theologians who believed the time was close. Their students were eager to be first to discover the promised Qá'im, and there were a number of people who gained temporary fame by announcing that they were the Báb, or Gateway to this expected holy personage. The spotlight for all but one was short-lived.
Mírzá 'Ali-Muhammad, a young merchant in Shíráz, Persia (Iran), met with one of those students wandering throughout the land searching for the Promised One, and during the evening and night of May 22 and the early morning hours of May 23, declared His station and mission. Part of the long night was spent in revealing and writing a series of essays of such erudition that scholars of the time were amazed. The Báb was absolutely fearless in His mission to prepare the world for Bahá'u'lláh, Whom He referred to as "Him Whom God would make manifest." The changes which He made to certain Islamic laws, as well as the huge numbers of followers who flocked to his Cause, annoyed and alarmed the local clergy, eventually resulting in outright repression. Thousands upon thousands of Bábis were tortured and killed, the Báb imprisoned and executed.
All that followed was still in the future that evening of May 22, 1844. The story is quite amazing, but too long to quote here. See links below for further reading.
The importance of the day to Bahá'ís is described this way: "The appearance of the Báb resembles the dawn, for the dawn holds the promise of the sun. The dawn of the Báb promised the rising of the sun of truth that is to envelop the whole world. The Báb in his writings heralded the advent of Bahá'u'lláh." ... It is a blessed day and the dawn of manifestation, for the appearance of the Báb was the early light of the true morn, whereas the manifestation of the Blessed Beauty, Bahá'u'lláh, was the shining forth of the sun. Therefore, it is a blessed day, the inception of the heavenly bounty, the beginning of the divine effulgence. On this day in 1844 the Báb was sent forth heralding and proclaiming the Kingdom of God, announcing the glad tidings of the coming of Bahá'u'lláh and withstanding the opposition of the whole Persian nation. - 'Abdu'l-Bahá, Divine Philosophy, p. 51-2
In daily life, Bahá'ís are exhorted to study and endeavor to improve not only their own character but also contribute to the betterment of society as a whole by translating the Writings of their faith into personal action. "Consider how the Báb endured difficulties and tribulations; how He gave His life in the Cause of God; how He was attracted to the love of the Blessed Beauty, Bahá'u'lláh; and how He announced the glad tidings of His manifestation. We must follow His heavenly example; we must be self-sacrificing and aglow with the fire of the love of God. We must partake of the bounty and grace of the Lord, for the Báb has admonished us to arise in service to the Cause of God, to be absolutely severed from all else save God during the day of the Blessed Perfection, Bahá'u'lláh, to be completely attracted by the love of Bahá'u'lláh, to love all humanity for His sake, to be lenient and merciful to all for Him and to upbuild the oneness of the world of humanity. Therefore, this day, 23 May, is the anniversary of a blessed event. - 'Abdu'l-Bahá The Promulgation of Universal Peace, p. 139