Program.cs is the entry point for the web application; everything starts from here. As we mentioned in the chapters before, the .NET Core host can only run console applications. So, the web app is a console application too.
project.csproj is an XML-based project configuration file. It contains all the package references and the build configuration.
Startup.cs is not exactly new. If you already used OWIN, you probably know the role of this class, but we can definitely say if the Program.cs is the entry point of the .NET Core app, Startup.cs is the entry point of ASP.NET Core application (previously we were using the global.asax file).
web.config is still here, but it's almost empty and only used to tell Internet Information Service (IIS) to process all requests using the ASP.NET Core handler.