You get what we call high-level features, which are basically abstract representations of the parts that carry information in the image you want to classify.
Imagine you want to classify a car. The image you feed your network could be a car on a road with a driver and trees and clouds, etc. The network, however, if you've trained it to recognize cars, will try to focus on parts of the image regarding a car. The final layers will have learned to extract an abstract representation of a car from the image (this means a low-resolution car-like shape). Now your final FC layers will try to classify the image from these high-level features. In this example, you would have an FC layer that learns to classify a car if this this abstract car-like figure is present in the image. Likewise, if it isn't present it won't classify it as a car. By accessing these high-level features, you essentially have a more compact and meaningful representation of what the image represents (based always on the classes that the CNN has been trained on).
By visualizing the activations of these layers we can take a look on what these high-level features look like.
The top row here is what you are looking for: the high-level features that a CNN extracts for four different image types.