Answer by taking a quote from the following article:

Jane was probably born at Wulfhall, Wiltshire, although West Bower Manor has also been suggested, the daughter of Sir John Seymour and Margery Wentworth. Her birth date was not recorded, but it is generally estimated as occurring in or around 1508. Through her maternal grandfather, she was a descendant of King Edward III's son Lionel of Antwerp, 1st Duke of Clarence. Because of this, she and King Henry VIII were fifth cousins.

Jane Seymour's labour had been difficult, lasting two nights and three days, probably because the baby was not well positioned. After the christening, it became clear that she was seriously ill. She died on 24 October 1537 at Hampton Court Palace. Within a few weeks of the death of Queen Jane, there were conflicting testimonies concerning the cause of her demise. In retrospect from the current day, there are various speculations that have been offered. According to King Edward's biographer, Jennifer Loach, Jane's death may have been due to an infection from a retained placenta. According to Alison Weir, Jane may have succumbed to puerperal fever following a bacterial infection contracted during the birth.  Jane Seymour was buried on 12 November 1537 in St. George's Chapel at Windsor Castle after the funeral in which her stepdaughter, Mary, acted as chief mourner. A procession of 29 mourners followed Mary, one for every year of Queen Jane's life. Jane was the only one of Henry's wives to receive a queen's funeral.  The following inscription was above her grave for a time:  After her death, Henry wore black for the next three months. He married Anne of Cleves two years later, although marriage negotiations were tentatively begun soon after Jane's death. He put on weight during his widowerhood, becoming obese and swollen and developing diabetes and gout. Historians have speculated she was Henry's favourite wife because she gave birth to a male heir. When Henry died in 1547, he was buried beside her, on his request, in the grave he had made for her.

What illness did she have?
Jane's death may have been due to an infection from a retained placenta.