A plain feedforward network (MLP or CNN) processes a fixed-size input in one shot — it has no notion of 'order' or 'what came before.' But language, audio, and time series are inherently sequential: the meaning of a word depends heavily on the words before it. Recurrent neural networks (RNNs) were the first widely-used architecture built specifically to handle this.
The core idea: a running memory
An RNN processes a sequence one element at a time, maintaining a hidden state — a vector summarizing everything relevant it has seen so far. At each step, it combines the new input with its current hidden state to produce an updated hidden state, which then gets passed to the next step.
h₀ (initial state)
read x₁ → h₁
read x₂ → h₂
read x₃ → h₃
output from final hₜ