In general Web Server's is responsible for accepting and fulfilling requests from clients.
A web server‘s fundamental job is to accept and fulfill requests from clients for static content from a website (HTML pages, files, images, video, and so on). The client is almost always a browser or mobile application and the request takes the form of a Hypertext Transfer Protocol (HTTP) message, as does the web server’s response.
Lately you can find many web servers like Apache or Nginx.
Kubernetes Ingress is an API object. In IBM blog - What is Kubernetes Ingress and why is it useful?
Kubernetes Ingress is an API object that provides routing rules to manage external users' access to the services in a Kubernetes cluster, typically via HTTPS/HTTP. With Ingress, you can easily set up rules for routing traffic without creating a bunch of Load Balancers or exposing each service on the node. This makes it the best option to use in production environments.
Also in Kubernetes Ingress Docs you can find that Kubernetes Ingress needs Ingress Controller.
You must have an Ingress controller to satisfy an Ingress. Only creating an Ingress resource has no effect.
There are many ingress controllers like Nginx, Ambassador, Apache, etc.
To sum up:
To use Ingress you need some Web Server as Ingress Controller.
Kubernetes Ingress is an Kubernetes object which helps user to configure Web Server (like Nginx) in Kubernetes Clusters.
As you pointed in documentation it allows you to configure some HTTP/HTTPS routing, traffic load balancing, terminate SSL / TLS, etc.
Ingress exposes HTTP and HTTPS routes from outside the cluster to services within the cluster. Traffic routing is controlled by rules defined on the Ingress resource.
