Vaisakhi is kept on 13 or 14 April and is two things at once, and the older of the two is agricultural.
It is the spring harvest festival of the Punjab, marking the ripening of the rabi crop, and it is the new year in several regional solar calendars across South Asia, the same solar moment is Puthandu in Tamil Nadu, Bohag Bihu in Assam, Pohela Boishakh in Bengal and Vishu in Kerala. The date is set by the sun's entry into the sidereal sign of Aries, which is a solar reckoning, not a lunar one, and this is why Vaisakhi has a nearly fixed Gregorian date while most South Asian festivals do not.
Its Sikh significance is dated and specific. On Vaisakhi in 1699, at Anandpur, Guru Gobind Singh is recorded as founding the Khalsa: calling for volunteers willing to give their heads, initiating five who came forward, then receiving initiation from them in turn, and instituting the five articles of faith and the shared names Singh and Kaur. It is the constitutive event of Sikh identity as it now exists.
The choice of an existing festival day was practical, a large gathering was already assembled, and this is the ordinary way religious calendars are built. It is not an absorption of a pagan observance, and the tradition has never presented it as anything other than what it was.
The date is also the anniversary of the Jallianwala Bagh massacre of 13 April 1919, when troops fired on a crowd gathered in Amritsar at the festival.