The key words here are priors and scale. As a simple example, imagine you're trying to predict a person's age from a photograph. With a dataset of images and ages, you could train a deep-learning model to make the predictions. This is objectively really inefficient because 90% of the image is useless, and only the region with the person is actually useful. In particular, the person's face, their body and maybe their clothing.
On the other hand, you could instead use a pre-trained object detection network to first extract bounding boxes for the person, crop the image, and then pass it through the network. This process will significantly improve the accuracy of your model for a number of reasons:
1) All of the networks resources (i.e. weights) can focus on the actual task of age prediction, as opposed to having to first find the person first. This is especially important because the person's face contains useful features. Otherwise, the finer features that you need may get lost in the first few layers. In theory a big-enough network might solve this, but it would be woefully inefficient. The cropped image is also considerably more regular than the original image. Whereas the original image has a ton of noise, its arguable the discrepancies in the cropped image are much more highly correlated with the objective.
2) The cropped image can be normalized to have the same scale. This helps the second network deal with scaling issues, because in the original image, people can occur near or far away. Normalizing scale beforehand makes it so that the cropped image is guaranteed to have a person in it that fills the full cropped image (despite being pixilated if they were far away). To see how this can help scale, a cropped body that's half the width and height of the original image has 4x less pixels to process, and hence the same network applied to this image would have 4x the original network's receptive field at each layer.
For example, in the kaggle lung competition, a common theme in the top solutions was some kind of preprocessing on lung images that cropped them as much as possible and isolated the components of each lung. This is especially important in 3D images since the effect is cubic: by removing 20% of each dimension, you get rid of nearly half the pixels!