Insanity was a condition of mental instability in sentient beings. It was colloquially referred to as madness or going crazy.
Gideon Crane, believing himself to be the Doctor, asserted that "madness" was simply a matter of one person's reality not agreeing with another's own reality. In such cases, one or both of them was said to be mad, whereas two people experiencing a shared delusion, or both deceived, might well call themselves sane. (AUDIO: Minuet in Hell)
After falling into an abyss on Kastria, the version of Eldrad that was regenerated from the hand was driven mad in his solitude. He talked to the dust that surrounded him - the remains of long-dead Kastrians. (AUDIO: Eldrad Must Die!)
When Eric Klieg and the Brotherhood of Logicians attempted to awaken the Cybermen in a bid to obtain power, the Second Doctor extolled Klieg's genius and brilliance. When Klieg responded positively and longingly to the concept of world domination, the Doctor dropped the act and concluded: "Well now I know you're mad. I just wanted to make sure." (TV: The Tomb of the Cybermen)
Insane Daleks were imprisoned in the Dalek Asylum. This planet was destroyed by the Parliament of the Daleks when its force field was lowered by the Oswin Oswald. Several of the Dalek inmates were driven mad after surviving encounters with the Doctor. (TV: Asylum of the Daleks)
The Ninth Doctor declared the Dalek Emperor's army of Daleks bred from human remains to be insane, "driven mad by their own flesh". He claimed their hatred of their own existence made them deadlier than ever. (TV: The Parting of the Ways)
The Cybermen did not understand the concept. (AUDIO: Return of the Cybermen) Their own emotions were suppressed to prevent them from contemplating their own conversion, as this realisation would drive the being inside insane. (TV: The Invasion, The Age of Steel)