A cult of personality or personality cult arises when a country's leader uses mass media to create a larger-than-life public image through unquestioning flattery and praise. The term often refers as well to leaders who did not use such methods during their lifetime, but are built up in the mass media by later governments. Cults of personality are often found in dictatorships but some can be found in some democracies as well.
A cult of personality is the same as from general hero worship in that it is specifically built around political leaders. However, the term cult of personality is often applied by analogy to refer to adulation of non-political leaders; an argument could easily be made, however, that the only notable differences to be found between the terms "hero worship," "cult of personality," or even, more simply, excessive admiration are largely in the context of the person making the accusation.

Background
The criticism of personality cults often focuses on the regimes of Mussolini, Hitler, Stalin, and Mao. During the peak of their reigns, these leaders appeared as god-like infallible rulers. Their portraits were hung in every home or public building, and artists and poets were legally instructed to produce only works that glorified the leader and their political movements. The term cult of personality comes from Karl Marx's critique of the "cult of the individual" - expressed in a letter to German political worker, Wilhelm Bloss. In that, Marx states thus:
From my antipathy to any cult of the individual, I never made public during the existence of the [1st] International the numerous addresses from various countries which recognized my merits and which annoyed me... Engels and I first joined the secret society of Communists on the condition that everything making for superstitious worship of authority would be deleted from its statute.
Nikita Khrushchev recalled Marx's criticism in his 1956 "Secret Speech" denouncing Stalin to the 20th Party Congress:
Comrades, the cult of the individual acquired such monstrous size chiefly because Stalin himself, using all conceivable methods, supported the glorification of his own person. . . . One of the most characteristic examples of Stalin's self-glorification and of his lack of even elementary modesty is the edition of his Short Biography, which was published in 1948.. A US religious freedom investigation confirmed Martin's observation that children learn to thank Kim Il-sung for all blessings as part of the cult.