A FCN is a convolutional network made up mostly from convolutional layers, which doesn't change the dimensionality of the data as it passes through it. E.g. a 2D FCN is such that a 2D input image remains 2D as it passes through the network, although it typically changes the number of channels ("feature maps") and resolution. In contrast, a CNN for classification at some point "flattens" the data (e.g. turns an image into a vector). Besides convolutional layers, a FCN typically contains downsampling and upsampling layers, as well as skip connections. It is a very common architecture for semantic image segmentation.