Machine learning: How is RELU used in the convolutional layer?

I know that when it comes to artificial neural networks, RELU produces a value based on the weighted sum of the inputs plus a term of bias. However, this logic does not seem to apply to convolutional neural networks.

When observing the ResNet architecture, the outputs of convolutional neural networks (what I think are feature maps) are added to the x input, and then RELU is applied. What exactly does the RELU function do in this case? Do convolution layers generate entity maps, or something else?