Your question is actually a bit too ambiguous and wide. You can in fact run Java code at any machine you like, regardless of the language you programmed the webbased interface in. You can for example create a PHP based website which interacts with a "backend" Java application (the "command line application" as you call it). The only requirement is to have a JRE at the server machine. Then basically everything as web interface suffices: CGI, PHP, ASP, Python, etcetera, you name it. As long as it has access to the underlying commandline runtime, which is in the PHP example to be done by exec()
.
But Java, actually Java EE, also provides a web application programming interface: the JSP/Servlet API, the web component of the large Java EE API. This make integration with the "commandline Java application" much more seamless. You can basically just put your application in the classpath and import/access/use it in a Servlet
class the real Java way:
YourApplication app = new YourApplication();
Result result = app.doStuff();
// ...
To be able to run JSP/Servlet (JSP is at end actually also a Servlet), you need a concrete implementation of the Servlet API (the whole Java EE is just an abstract specification). Apache Tomcat is good to start with, the other popular alternative being Eclipse Jetty. Those are 'simple' servletcontainers which implements the Servlet API, with Jetty being a more embedded approach of it (you can configure and run it as a "plain vanilla" Java Application). But if you need to support/cover the other aspects of the Java EE API as well, then you need an application server, such as Sun Glassfish or JBoss AS (both which by the way uses Tomcat as the servletcontainer part).
To learn more about JSP/Servlet, I can recommend the Coreservlets.com tutorials.