Heart Virus is a deadly virus that Future Goku and Present Goku both contract in November or December of Age 766. The name of the virus is never stated, and is generally referred to as "Heart Virus".
Unfortunately, Future Goku dies from the Heart Virus in Future Trunks' alternate timeline. Six months following his death, the androids appear and murder all of the Z Fighters with the exception of Future Gohan, thus sparking the events of Dragon Ball Z: The History of Trunks as well as the Trunks, Androids, and Cell Sagas.
In the main timeline, Future Trunks arrives from the future and gives Goku the antidote to the Heart Virus (the virus is incurable when Goku first gets it, but a cure is developed soon afterward; it was just too late for Goku). However, his presence in the past causes history as he knows it to change drastically. One major change is that Goku does not contract the heart virus when he was originally supposed to, but instead it appears several months later during his fight with Android 19 in May of Age 767. Goku is saved from death by Vegeta and taken home to receive the antidote. Ten days later, the virus is successfully cured, and Goku re-joins the fight against the androids and the new threat, Cell.
It is never explained why or how Goku contracted the virus six months after his alternate timeline counterpart, although a possible explanation is that Goku, knowing of the androids' arrival, was at home, training, whereas Future Goku, thinking that all was well, was out having fun with his family, where he contracted the virus. Main Timeline Goku appears to have contracted the virus while in Sasebo (the city where the Androids first appeared), as he was noticeably exhausted after merely flying away from the city, justifying that he did not catch it while training for the Androids, since Goku's house is on Mount Paozu. Alternately, Goku's training may have simply postponed the virus as he was in better health.
Another possible reason is because Goku originally defeated Frieza and King Cold on Earth, not Future Trunks, therefore lessening the wear and tear on his heart. While going Super Saiyan seems to speeds up the process, when not Super Saiyan the infection is very slow.
The Heart Virus appears in Dragon Ball Z: Budokai, Budokai 2, Budokai 3 and Infinite World where it is renamed "Viral Heart Disease", and is a special technique that can only be used by equipping in the "custom" menu in the character selection screen. It takes 2-3 of the 7 technique slots, in game it causes both the user and opponent's health to deplete continuously, until only half of their last health bar is left. The user and opponent can avoid taking damage by equipping "Vaccine", a single slot technique which nullifies Viral Heart Disease's effect.