Happiness induction is Didyme's raw ability to bring joy to oneself and everyone close to her.
According to Stephenie Meyer, this power was only possessed by Didyme, Aro's younger sister, which made the Volturi members around her happy during her time of existence. But the most benefactor of this talent of hers was Marcus, one of the Volturi leaders, who became her mate. This power seemingly released an aura of happiness that naturally affected everyone around her wherever she went, and so people were easily to attach themselves to her.
Happiness induction could also bring happiness to Didyme, as well as those around her.
According to The Twilight Saga: The Offical Illustrated Guide, Didyme showed this power even in human form, though it was much more dormant before she became immortal.
After she became a vampire, this power manifested much more clearly, allowing those around her to be easily affected by her aura. When Aro first transformed her, they also brought in the first members of the Volturi guard. None of these subordinates lasted longer than a few centuries, though.