Migrate HTTP handlers and modules to ASP.NET Core middleware explains the difference between request pipelines in ASP.NET Core and ASP.NET 4.x and provides additional middleware samples. When a middleware short-circuits, it's called a terminal middleware because it prevents further middleware from processing the request. Each middleware component in the request pipeline is responsible for invoking the next component in the pipeline or short-circuiting the pipeline. These reusable classes and in-line anonymous methods are middleware, also called middleware components. An individual request delegate can be specified in-line as an anonymous method (called in-line middleware), or it can be defined in a reusable class. Request delegates are configured using Run, Map, and Use extension methods. The request delegates handle each HTTP request. Request delegates are used to build the request pipeline.
Middleware is software that's assembled into an app pipeline to handle requests and responses.