Telegram's security options allow you to create private chats with other users, which means that your conversations with them are completely encrypted and aren't saved or stored on Telegram's servers. And you can activate a 'self-destruct' feature so that your messages are erased every X amount of time.
Aside from those privacy features, Telegram offers basically the same service as any other instant messaging system: group chats, file sharing, personalized notifications, etc.
Telegram is an instant messaging tool that shares many similarities - including its appearance - with WhatsApp. Still, the additional privacy that it provides could be very attractive to many people. Don't want conversations with certain contacts to be saved? Set them to self-destruct after ten seconds, and you're all set!