Mahavira (Vardhamana Mahavira) was born on the 13th day of the bright half of the month of Chaitra in the Jain calendar (Chaitra Sud 13). This day is celebrated by Jains as Mahavir Jayanti or Mahavir Janma Kalyanak. The traditional year given in Jain texts is 599 BCE. Some Digambar texts give slightly different year estimates (e.g., 615 BCE), but 599 BCE is the widely cited figure in many Śvetāmbara sources. He was born in Kundagrama (today often associated with near Vaishali, Bihar) to King Siddhartha and Queen Trishala. You can read more here and here

Notes:

• Śvetāmbara and Digambara traditions agree on the festival and the birth as a key event, but some details (like exact year) may differ slightly between traditions.
• The date shifts each year in the Gregorian calendar because it follows the lunar-hindi calendar (the Trayodashi tithi of Chaitra).