Destiny's neural link is capable of manipulating the minds of its crew and causing them to see and hear things which are not real while they are fully conscious. So far, it has only used this ability to project the images of people into the minds of its crew for the purposes of communication, though it is likely that it can project any other visual or auditory sensation. It does not appear capable of manipulating the senses of touch, taste or smell, however - the former having being attempted with no success. This system is not limited to use by the Destiny AI either, as the minds of Dr. Amanda Perry and Ginn, uploaded to the Destiny database and running as programs in its mainframe, used it to communicate with their friends aboard the ship.
It was theorized by Dr. Nicholas Rush that the ship can also monitor the thoughts and feelings of the crew using the neural link, and does so for the purposes of understanding its crew better. This was especially important when the AI was piloting the ship, before the discovery of the master code.
Although communication is limited, as described above, whilst the user is fully awake; Destiny can affect all senses whilst the user is asleep or unconscious. In combination with its apparently flawless simulation program, the ship can place the user in a virtual reality world. Despite being asleep or unconscious, users experience and remember the simulation as if totally awake. (SGU: "Trial and Error")
The first known use of the neural link was when Lt. Tamara Johansen was shot during the Lucian Alliance invasion of Destiny. Unconscious, the ship placed her in a seemingly perfect simulation of a log cabin on Eden. She was told that her baby was safe, and this gave her comfort once she recovered. It was theorized that this was due to Destiny's realization that she, as a medic, was important to the survival of the crew; and so it attempted to solve her emotional problems to allow her to work without emotional distraction. (SGU: "Intervention")
When Dr. Nicholas Rush discovered the Destiny Bridge, he had regular confrontations with Dr. Jeremy Franklin and an image of his wife Gloria Rush using the neural link. Whilst he now believes the former was a stored consciousness in the Destiny database, the origin of the latter in unknown, though it is likely a creation of the ship, based on Rush's own memories. (SGU: "Aftermath", "Pathogen", "Trial and Error", "Hope")
For an unknown reason, the Destiny AI exposed Colonel Everett Young to a virtual simulation using the neural link. Every time he fell asleep, he was forced to act in a no-win scenario involving Nakai surrounding the ship and demanding the surrender of Chloe Armstrong to them. Whatever course of action he chose, it resulted in ether destruction or capture of the ship by their overwhelming forces. It was this simulation which led to the discovery of the ship's neural link, prompting Rush to disable certain aspects of it. (SGU: "Trial and Error")
When Dr. Amanda Perry and Ginn were uploaded into Destiny's database, they used the neural link to communicate with their friends - though were unable to have any physical contact due to the limitations of the system when the user is awake. (SGU: "Hope", "Seizure")