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.
While bluepills have their headjack in use at all times while inside their pods, permanently connected to the Matrix through the power plant, a redpill uses their headjack only during their periodic missions to free minds as part of their rebellion against the Machines.
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.
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." Removal of the probe from the headjack before the individual has a chance to properly "jack out" of the Matrix results in instantaneous death, a fate that befalls both Switch and Apoc at the hands of Cypher.
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.
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.
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.