Josh Starmer explains recurrent neural networks, emphasizing their role as a foundation to more advanced networks like Long Short-Term Memory Networks and Transformers. He discusses the concept by presenting a scenario where a neural network is used to predict stock prices in a simplified context called StatLand. Stock prices fluctuate over time and having a larger dataset is advantageous for predictions. Starmer illustrates that to predict stock prices effectively, the neural network must be adaptable to varying amounts of sequential data. For instance, predicting the stock price of a company with a longer trading history requires using data from previous days, while a company with a shorter history limits the available data. This adaptability is crucial and differentiates recurrent neural networks from traditional ones that rely on fixed input values. The summary encapsulates the key points about how recurrent neural networks function and highlights their importance in handling sequential data for tasks like stock price prediction.