신나다 is being excited, buzzing, having a great time, and the 고 clause gives what leads into it. Three of these lines make the same joke of someone thrilled because they do not know better: happy without knowing what is coming, splashing about not realising he has been tricked, chatting away thinking it was good news. The rest are straightforward, such as getting excited because someone finally let him, or dancing after a long time and laughing a lot.