In just a few minutes you can easily deploy Docker Container Images using just a context menu from the repositories blade of the Azure Container Registry.
Azure Container Instances allow you to deploy Container Images directly without first provisioning VMs, Container Orchestrators, or any other container infrastructure. With Azure Container Instances, you pay just for what you use. Azure Container Instances are not a replacement for Container Orchestrators, in fact you may run your Container Orchestrator hosts on Container Instances to give burstable resources. For more about Azure Container Instances, see this post from Corey: Fast and Easy Containers: Azure Container Instances
Seeing is believing, so here's a video on just how easy it is.