This bloody, disgusting effect was popularized by Judge Harold T. "Harry" Stone and remains a disturbing classic.
The magician produces a large needle -- perhaps a foot long -- and demonstrates for the audience that it is ungimmicked. The magician's bare forearm is then presented and also demonstrated to be ungimmicked. After everyone is satisfied, the magician pushes the needle through the forearm's muscle, slowly and deliberately, with much running blood, grimaces of pain, etc.
In some versions of the trick, the needle has a red ribbon attached to its eye, which is also drawn through the arm. This may be followed by the production of a great length of multicolored streamers from the hole in the arm (particularly at children's shows).
Before the trick, flame and alcohol are used to completely sterilize the needle. The magician's arm is rubbed with alcohol immediately before the performance, and any ribbon used is actually sterile gauze. The trick then proceeds as described above.
How, you ask, can a magician perform such a feat without horrific pain and the serious possibility of permanent physical damage? Well, a serious, doctorate-level study of anatomy helps the magician avoid puncturing anything that won't eventually heal, and the sterilization of equipment, immediate bandaging after the performance, a current tetanus shot, and rounds of antibiotics keep the chance of infection at a minimum, but you're pretty much stuck with the horrific pain (no pun intended).
Magicians who want to perform this effect frequently sometimes have a plastic tube surgically inserted in their arm that the needle can be painlessly and repeatedly passed through, but this requires the magician to also make use of fake blood during the performance and frankly most don't consider it to be worth the bother.
It is not recommended that this trick be performed by hemophiliacs.