I have a friend who has this pan. What is it used for?
Your friend has an omurice pan. Omurice is a type of Japanese omelet. From Wikipedia:
Omurice or omu-rice (オムライス Omu-raisu) is an example of yōshoku (a Western-influenced style of Japanese cuisine1) consisting of an omelette made with fried rice and usually topped with ketchup. With omu and raisu being contractions of the words omelette and rice, the name is an example of Gairaigo. It is a popular dish both commonly cooked at home and often found at western style diners in Japan.
Omurice is said to have originated around the turn of the 20th century at a western style restaurant in Tokyo's Ginza district called Renga-tei, inspired by chakin-zushi. The dish was brought to Korea and Taiwan, and it is popular cuisine. In Japan children, in particular, enjoy omurice, and it is often featured in okosama-ranchi (お子様ランチ) or kids' meals.1
This picture shows how it would be used: