What is difference between feed forward neural network and LSTM?
A feed-forward neural network looks like this:

input -> hidden layer 1 -> hidden layer 2 -> ... -> hidden layer k -> output.

Each layer may have a different number of neurons, but that's the architecture.

An LSTM (long-short term memory cell) is a special kind of node within a neural network. It can be put into a feedforward neural network, and it usually is. When that happens, the feedforward neural network is referred to as an LSTM (confusingly!).

So how does an LSTM work? Have a look at my answer here: Forget Layer in a Recurrent Neural Network (RNN) -

tl;dr: an LSTM cell has three gates, each of which is used to modulate its input in some way: an input gate, a forget gate, and an output gate. It has a "memory" and an output that get modified by the gates. That is, within a single LSTM cell:

(input &amp; previous cell state) ->  (input &amp; forget gates) -> (update cell state)

(input &amp; previous cell state &amp; updated cell state) -> (output gate) 

You can stack these cells in many different configurations. So there is no single "LSTM network" - rather a set of many possible architectures that can be built from these basic nodes.

Hope that gets you started!