What you are asking to do is to synchronize your calendar between Android and your website. This answer is along similar lines and may help.
Essentially you need a way to communicate 1) the fact that there have been changes, and 2) a way to transfer the data. You want to communicate the fact that the calendar changed in a minimum of bytes, and do it often. So you could have some kind of checksum that every minute or 5 minutes, you go and ask for the new checksum, if it has changed, then request the calendar data via JSON or some other way.
An example interface for the service would be:
import javax.ws.rs.GET;
import javax.ws.rs.Path;
@Path(value = "/calendar")
public class CalendarResource {
@GET
@Path("/{userid}")
public Response getChecksum(@PathParam("userid") String userid) {
String checksum = "test"; // do some calculation or fetched cached one
return checksum;
}
@GET
@Path("/{userid}")
public Response getCalendar(@PathParam("userid") String userid) {
String calendar = "test"; // do some calculation or fetched cached one
return calendar;
}
}
You can find dropwizard tutorials here and here
You can find how to call the service here
What you need to do is read the tutorials, build a simple version and then when you have troubles look for answers like the above or ask a new question and post your (almost) working code.