An App Service Environment v2 is a fully isolated and dedicated environment for securely running Azure App Service apps at high scale, including Web Apps, Mobile Apps, and API Apps. It is essentially a deployment of the Azure App Service into a subnet of your network, so think of it as your private Platform-as-a-Service environment in the cloud.
App Service Environment v2 release announcement (blog):
Introduction to App Service environments (docs):
App Service (overview):