Hi Liam, I don't know where you learnt your Mandarin but it's really a history that we Chinese were that serious about inviting somebody else to home for a dinner :)
I think your teacher must wanna you to learn our Chinese culture deeply, so he raise such a question in front of you :)
Actually during past time, it's really a matter if somebody invite you to his home for eating, it really means that he's treating you very seriously maybe as a brother :) You know we Chinese shows great respect to our parents, in traditional way, once somebody's willing to take you to see his parents(no matter it's a male or female friend), it means at least he/she thinks you are good enough to be introduced to his/her parents or nowadays may his wife or husband ;)
But there's really nothing to be nervours, usually for the first time we go to a friend's home, we usually take some simple gifts such as some timing fruits or vegetables, normally just for enriching the dinner table :) or something specially representative your greeting/regards :)