What is the kestrel web server and how does it relate to IIS / IIS Express?

I come from developing apps on IIS Express and hosting them on an IIS web server. With ASP.NET Core I have a dependency on Microsoft.AspNetCore.Server.Kestrel and my startup has .UseServer("Microsoft.AspNetCore.Server.Kestrel"). But when I run my website, I still get the IIS Express icon in the system tray. Someone asked me if I was using IIS Express or Kestrel and I didn't know what to say!

I don't have any cross-platform requirements as I develop on a PC and host in Azure, so I'm confused if I even need Kestrel, but it doesn't seem like there's an alternative - even the simplest samples use Kestrel.