The phage was a disease that afflicted the Vidiians, killing thousands daily for approximately 2,000 years. The disease was highly adaptive to nearly every new form of medical treatment, and adapted so fast that their "immunotechnology [could not] keep up." It consumed the Vidiians, at first disrupting their genetic code, then devouring their body tissues and destroying cellular structures. One of the early symptoms of the disease was excruciating joint pain. Some victims had been known to die simply from the agony itself, and euthanasia of afflicted persons was common. (VOY: "Phage", "Faces")
The Vidiians survived in the short term by making extensive use of transplantation and organ piracy, using transporter technology to literally steal healthy organs from the bodies of their owners. Increasingly desperate, the Vidiians resorted to kidnapping members of other species and experimenting on them.
The term "phage" is short for bacteriophage. The term "phage" itself literally means "to eat." A bacteriophage is a virus that reproduces within a bacterium - it infects bacteria by attaching a hollow protein tail to a bacteria cell wall, injecting DNA (or sometimes, RNA) into the cell. Bacteriophages live at the expense of the bacteria they inhabit, and in most cases eventually kill their bacterial hosts.