VDT stands for "virtual" delirium tremens, in the fictional world of The Matrix.
Conventional, real-world delirium tremens (colloquially, the DTs, "the horrors", "the shakes" or "rum fits") is a condition usually associated with complete alcohol withdrawal. However, delirium tremens can appear after a rapid reduction in the amount of alcohol being consumed by heavy drinkers, and also occurs as a complication of benzodiazepine and barbiturate withdrawal. It only occurs in individuals with a history of constant, long-term alcohol consumption. Delirium tremens typically manifests about 18 to 24 hours after discontinuation of alcohol consumption, but can appear on the second or third day of abstinence.
The symptoms include severe, uncontrollable tremors of the extremities and intense hallucinations such as insects, snakes or rats. These may be related to the environment, e.g., drawings on wallpaper that the patient would perceive as giant spiders ready to attack her or him. Unlike hallucinations associated with schizophrenia, delirium tremens hallucinations are primarily visual, but associated with tactile hallucinations such as sensations of something crawling on the subject. Other symptoms include agitation, confusion and the associated alcohol withdrawal fits. Secondary symptoms can be anxiety, panic attacks or paranoia.
In the world of The Matrix, Zionists (real-world humans fighting the machines that have enslaved the vast majority of humanity who are kept contained in the Matrix) who are completely submerged into a virtual environment could suffer virtual delirium tremens, or withdrawal symptoms from leaving the virtual environment.
In the film The Matrix Revolutions, the character of Maggie uses the term VDTs when asked about the status of Bane, whose real-world body is under control of Agent Smith
The Hammer's infirmary
Maggie, the Hammer's nurse: Thought you could use something to eat.
Trinity Thank you.
Maggie: Any change?
Trinity No. How's he? (referring to Bane)
Maggie: He's going to be fine, at least until he wakes up.
Trinity What do you mean?
Maggie: The Captain has some questions for him. He better have some good answers. You see these cuts? I think they're self-inflicted.
Trinity Why?
Maggie: VDTs, maybe. I don't know. But like I said, the answer had better be good.
VDTs are mentioned in a later scene, after Bane awakes and is interrogated by Morpheus, Trinity and the command crew of the Hammer, in the Hammer's mess hall.
Bane: I really wish I could help, but I just... I don't remember any of it.
Roland, captain of the Hammer: What about the cuts on your arms? Those cuts are more than one day old.
Bane: Yeah, definitely. You're right about that, sir. They look like they might be self-inflicted. Why would I do something like that to myself? Unless, of course, I wasn't myself... but... if I'm not me, then who am I?
Roland: Has this man been tested for VDTs?
Maggie: Yes, sir, it was negative. But he is showing a lot of unusual neural activity. Some cross-synaptic firing as well as signs of recent trauma, with fresh fibrotic scarring throughout the cortex.
Roland: I want the truth, I don't care what it takes. Make him remember.