Not only is she completely oblivious of his inner feelings and thoughts, but she also seems to be blind to what is going on around her.

be 是系动词，表示"是"或"存在"的状态。 blind 本义是"失明的"，在这里用作形容词，表示"看不见的"，引申为"视而不见的"。 to 是介词，表示"对..."或"向..."的方向。 be blind to 是一个固定搭配，意思是"对...视而不见"，表示故意或无意地忽略某事。