A headjack is the term used to describe the small data port created on synthetically-grown humans who become connected to the neural-interactive virtual reality known as the Matrix.
Headjacks are located at the base of the skull, just above where the neck meets the back of the head. Approximately 1 inch in diameter, it probably provides room within the otherwise close quarters of the human cranium for a data probe approximately 8 inches in length and 20mm in diameter.
Communication by the headjack is probably a mixture of electrical and electromagnetic transmissions, where the headjack is the central interface, with perhaps thousands of tiny connectors or electrodes that meld into and throughout the brain, or woven through the central nervous system at the brain stem. It is possible that the Machines grew the human around the headjack and other body plugs, rather than inserting them at the time of the fetus' maturity.
When a redpill is freed from the Matrix, a Docbot is summoned, which proceeds to unpleasantly 'unscrew' the connection jack from the headjack port (along with the rest of the ports along the body) before flushing the human into the sewers.
The insertion of a data probe into a headjack does not appear to be an altogether pleasant sensation (though not necessarily painful): Morpheus warned Neo that the insertion of the data probe into his headjack for the first time outside of the pod would "feel a little weird." This is presumably because the data probe was not intended to be inserted and removed regularly.
Use within the Matrix Edit
Bluepills, human beings still hardwired into the Matrix via pods in the power plant, have their headjack in constant use and do not know of its existence. As humans are generally only expected to be disconnected from the Matrix upon death, the pod's data probe is very securely attached to the headjack.
Redpills use their headjacks as their primary means of accessing the Matrix, for periodic missions as part of their rebellion against the Machines. This is done via data probes similar to the pod's, but less securely attached, only being secure enough to prevent accidental removal. The headjack is otherwise unused.
The manner in which the headjack and data probe work has not been described in the "Matrix" film trilogy. However, it is plausible that the headjack includes a small electronic memory buffer that retains the RSI used by the "avatar", allowing the human to retain certain physical characteristics.
When an individual has a headjack inserted and is in the Matrix or other virtual location, their body is vulnerable to physical harm and tampering. Notably, if a headjack is removed by somebody in the Real World before the individual can "jack out" of the Matrix, they suffer instantaneous death by unknown cause, presumably massive neural damage. Switch and Apoc of the Nebuchadnezzar crew suffer this fate at the hands of Cypher; their real bodies simply die, while their RSIs collapse dead within the Matrix.
- As implied in the original script of The Matrix, the humans not only provide electrical power, but their brains become part of a massive biocomputing cluster that generates and maintains much of the Matrix itself.