The client’s request, remember, always includes a specific HTTP Method. If the HTTP Method is a GET, the service() method calls doGet(). If the HTTP request Method is a POST, the service() method calls doPost().
You probably won’t care about any HTTP Methods except GET and POST
Yes, there are other HTTP 1.1 Methods besides GET and POST. There’s also HEAD, TRACE, OPTIONS, PUT, DELETE, and CONNECT.
All but one of the eight has a matching doXXX() method in the HttpServlet class, so besides doGet() and doPost(), you’ve got doOptions(), doHead(), doTrace(), doPut(), and doDelete(). There’s no mechanism in the servlet API for handling doConnect(), so it’s not part of HttpServlet.
But while the other HTTP Methods might matter to, say, a web server developer, a servlet developer rarely uses anything but GET and POST.
For most (or probably all) servlet development, you’ll use either doGet() (for simple requests) or doPost() (to accept and process form data), and you won’t have to think about the others.