Used primarily in anatomic and botanical contexts. Being male, what immediately comes to mind is a scrotum, but there are many more bursiform things, including flowers (such as the ladyslipper) and seed pods (none come to mind at the moment). This word was coined in the 1830s from Latin bursa, meaning purse or bag -- at the time, and through the middle ages, a purse was a bag, or rather pouch, worn at the waist. It's the same root as gives us bursar, the treasurer (modern term: chief financial officer) of a college or university.
Under the vine, in the way of the passage, hung several purple bursiform sacs, which when touched gave off a putrid scent -- an effective security measure against raiders.