Sometimes instead of being henna, "black henna" is made using a chemical called PPD (P-Phenylenediamine), either on its own or combined with natural henna. In many people, this can lead to severe reactions including blisters, lesions, rashes, etc. Assuming it enters the body (which it can do via the skin), PPD toxins can collect in the internal organs. This damage, most often liver and kidney, can show up later, even if there are no external symptoms. In addition, PPD is a carcinogen (causes cancer), and artists should be concerned about breathing it in as exposure can lead to lung complications such as asthma.
In extreme cases, PPD exposure can cause DEATH.
PPD reactions sometimes happen within a day of the henna's application, but it is not unheard of for them to show up literally weeks, or even a month and a half later, even after the henna has largely faded — meaning that allergy spot tests are virtually useless. As well as being contained in some henna products, PPD is also contained in many "oriental black" hair dyes, which are often used by unscrupulous henna artists.
"Natural" hennas are not generally able to achieve a jet black effect; the best you'll normally get is dark browns. If your fresh henna becomes jet black within a few hours, worry! Assuming you visit a doctor or dermatologist, make sure to tell them that you may be having a PPD reaction — not all will know that PPD is an active ingredient in black henna.