The adversarial loss in a GAN represents the amount of information that the generator is able to trick the discriminator into believing is true.

"The adversarial loss influences whether the generator model can output images that are plausible in the target domain"$\rightarrow$ means that the generator model should output images that look like they could plausibly belong to the target domain. This is important because if the generated images look too fake, it will be difficult for the discriminator to learn to correctly classify them. It's the data that determines whether and how it improves.

In addition, the adversarial loss is based on the generator model's experience of its successes and failures in the data.