ASP.NET Core is the new version of the ASP.NET web framework mainly targeted to run on .NET Core platform. ASP.NET Core is a free, open-source, and cross-platform framework for building cloud-based applications, such as web apps, IoT apps, and mobile backends. It is designed to run on the cloud as well as on-premises. Same as .NET Core, it was architected modular with minimum overhead, and then other more advanced features can be added as NuGet packages as per application requirement. This results in high performance, require less memory, less deployment size, and easy to maintain.
ASP.NET Core applications can run on Windows, Linux, and Mac. So you don't need to build different apps for different platforms using different frameworks. ASP.NET Core no longer depends on System.Web.dll for browser-server communication. ASP.NET Core allows to include packages that we need for our application. This reduces the request pipeline and improves performance and scalability. It allows you to use and manage modern UI frameworks such as AngularJS, ReactJS, Umber, Bootstrap, etc. using Bower (a package manager for the web). ASP.NET Core web application can be hosted on multiple platforms with any web server such as IIS, Apache etc. It is not dependent only on IIS as a standard .NET Framework. ASP.NET Core application runs on .NET Core, which is smaller than the full .NET Framework. So, the application which uses only a part of .NET CoreFX will have a smaller deployment size. This reduces the deployment footprint.