What are Docker image layers

Question

I'm new to Docker and am attempting to figure out what exactly a Docker image is. Every definition of a Docker image utilizes the term "layer," but none of them appear to define what that term means.

From the official docker documentation:

We’ve already seen that Docker images are read-only templates from which Docker containers are launched. Each image consists of a series of layers. Docker makes use of union file systems to combine these layers into a single image. Union file systems allow files and directories of separate file systems, known as branches, to be transparently overlaid, forming a single coherent file system.

So, what exactly is a layer, and can someone provide any actual examples? What happens when these layers "snap together" to make an image?