Server in ASP.Net Core
An ASP.NET Core app runs with an in-process HTTP server implementation. The server implementation listens for HTTP requests
and surfaces them to the app as a set of request features composed into an HttpContext.
Default web server in ASP.Net Core
Kestrel is the default web server specified by the ASP.NET Core project templates.
To understand Kestrel, lets look into below figure(Ref: Microsoft Documentation)

Kestrel with IIS or IIS Express
Hosting Models in ASP.NET Core
There are 2 types of hosting models in ASP.NET Core i.e In-process Hosting and Out-of-process Hosting.
Before ASP.Net Core 2.2 we have only one hosting model which is Out-of-process
but after due to the performance we have In Process Hosting Model in 2.2+ versions
Summary
To summarise, Kestrel server is the default web server which is cross-platform
and support SSL . Hope you picked up a thing or two.
Cheers!