To understand recurrent networks, first you have to understand the basics of feedforward networks. Both of these networks are named after the way they move information through a series of mathematical operations performed at the nodes of the network. One feeds information in only one direction through every node (never touching a given node twice), while the other cycles it through a loop and feeds it back to the same node (kind of like a feedback loop). It is easily understood how the first kind is called a feedforward network, while the latter is recurrent.
Introduction to feedforward networks
Getting ready
The most important concept while understanding any neural network diagram is the concept of computational graphs...