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): https://docs.microsoft.com/en-us/azure/app-service/environment/intro
Introduction to App Service environments (docs): https://docs.microsoft.com/en-us/azure/app-service/environment/intro
App Service (overview): https://azure.microsoft.com/en-us/services/app-service/