They have huge advertising campaign going on here in India with top bollywood stars. I would still be surprised if they were doing good here. Why is there still a market for internet messengers? There are so many of them already. it's like image sharing apps.
Ok, here is what I have observed so far (I don't use Line myself):
1. Line works with your telephone number (if you have someones number you can send them a message)
2. Line allows you to send messages (free sms) and voice calls.
3. Line allows you to have friend groups.
But there also reasons specific to Asia (at least Thailand):
1. Line has a "cute look" and has smilie packs which you can buy (big images actually). Thais seem to love that. Westerners would probably find them childish.
2. Line has status messages. These seems to be used in quite an interesting way: to tell people something which you don't really want to tell them directly, e.g. "Stop being jealous. Change your life to make other people jealous.".