Which South Indian classical dance-drama's name means 'Story-Play'?

The correct answer is Kathakali. The name Kathakali comes from two Malayalam words: "katha", which means story, and "kali", which means play or performance. So Kathakali means "story-play", which describes the art well, since it is a dance-drama that tells stories through dance, gesture, expression, music and costume.

Kathakali tells stories mainly from the Ramayana, the Mahabharata and the Puranas, such as the stories of Nala and Damayanti, of Bhima and Draupadi, and of Krishna's mission of peace to the Kauravas. The texts of the plays, called attakathas, are written in Manipravalam (a mix of Malayalam and Sanskrit) by poets such as Unnayi Warrier (author of the famous Nalacharitham), Kottayam Thampuran and Irayimman Thampi. The actors do not speak. Instead, the story is sung by two singers at the back of the stage, while the actors act out every word through mudras (hand gestures), based on the Hastalakshana Deepika, and through highly expressive movements of the face and eyes. The actors wear spectacular, colour-coded make-up and costumes, which show the nature of each character: green for noble heroes, red and green for arrogant or evil characters, black for forest dwellers and demonesses, and so on. The performance is accompanied by drums such as the chenda and maddalam, and traditionally takes place at night, lit by a large oil lamp.

About the other options:

• Kuchipudi is named after the village of Kuchipudi in Andhra Pradesh.
• Mohiniyattam means "the dance of the enchantress", from Mohini, the female form of Vishnu.
• Bharatanatyam is often explained as a combination of Bhava (expression), Raga (melody), Tala (rhythm) and Natyam (dance), and is also linked with Bharata Muni, the author of the Natyashastra.