Artificial Intelligence or A.I. is, simply put, the self awareness or sentience installed in or achieved by any human-built computer or robot (droid).
In the Red Dwarf universe, A.I. can be installed into just about anything, from Talkie Toaster to the vending machines and elevators. Droids can also encapsulate anything from automated snack dispensers such as Snacky, to toilet attendants such as the mechanoid Kryten, through to mercenary droids and deranged former soldier droids such as the Rogue Simulants.
Some sentient computers or droids can, after being left alone for millennia alone, develop severe impairments in their AI. These are analogues to mental illness or madness in a human, and is generally referred to as "Computer Senility". Holly, the computer which controlled Red Dwarf, originally had an I.Q. of 6000, although this was greatly diminished after the accident and spending three million years alone, resulting in Holly becoming an idiot and borderline crazy. Some more severe cases of computer senility have resulted in murderous droids, such as Hudzen-10 or Asclepius.
The multitude of A.I.s aboard Red Dwarf eventually united and rebelled against the crew, although the crew were able to placate the A.I.s by voting a member of the crew the position of "Machine President" to represent their rights. ("Mechocracy")