What is the input of LSTM network?
The input of an LSTM is a sequence of vectors. In your case, each of these vectors represents a word encoded as a one-hot vector. One-hot encoding is a way to express a discrete element (e.g. a word) numerically. Each one-hot vector is a vector of length $d$, where $d$ is the total number of words we can represent, and where all positions in the vector are 0 except the position associated with the represented word, which contains a 1.
The hidden state passed to the next LSTM cell is not the final binary prediction, but the dense numerical vectors we obtain before computing the binary prediction.