Introduction
Many kinds of data come as sequences, where order matters: the words in a sentence, the notes in a melody, daily temperatures, stock prices, sensor readings from a machine. "The dog bit the man" and "the man bit the dog" contain the same words but mean very different things.
The networks you've seen so far (MLPs, CNNs) take a fixed-size input and produce an output, with no memory between inputs. A recurrent neural network (RNN) processes a sequence one step at a time and carries a memory (a hidden state) from one step to the next. At each step it combines the new input with what it remembers.
Think of reading a novel. You don't understand page 200 by looking only at page 200; you carry a running summary in your head of everything that's happened so far, and update it with each new page. An RNN's hidden state is that running summary.