Push Hand is very important in your Tai Chi training.
First understanding of Push Hands is to Develop your Listening Energy (Teng Jing.) Most people make the mistake of bypassing this. Until you can develop your Listening Energy, you will not be able to apply self defense application correctly.
Later stage is to develop your understanding of the BaFa.
Then to help develop you understanding of Self Defense Applications and Chin Na from your movements in your 4 Basic forms of Old Frame & New Frame.