I understand a Webservice application consists of the application server, Web server and database server. I have tomcat installed and using oracle as database.(all on the same machine). I am using jee as server technology. So tomcat is my Web server, oracle, my dB server, but what is my application server?
Tomcat is the application server because that is where your Java application lives (the back end if you prefer). If it provides the web pages then it is both your web and application server but in the modern world usually that is not the case. In most web services scenario your tomcat will provide some web service end points and the front end of the application (UI) will live on a separate server. That would be the web server and it can be something completely different - not even be java based. Just some UI calling your API.
You can have for example:
Web server running Angular app -> connected to Tomcat which runs your java app -> connected to the oracle