That is really what threads are for.  There are a million ways to do
this but the simplest is to wrap the code you want to run in another
thread in a Runnable and create a thread and start it.

// parent decides to run a task in another thread
Runnable r = new Runnable() {
    public void run() {
        // do your thing
    }
};
new Thread(r).start();
// the Runnable above is now running concurrently with the parent
// parent continues

Have you look at the Thread class?
http://java.sun.com/javase/6/docs/api/java/lang/Thread.html

Its quite possible, even easy.

One thing to consider though, is what happens if you get "slammed" by
traffic. Often times web containers will pool their main threads and
block incoming connections until a thread becomes available.  If you are
spinning off these child threads without any consideration, you may
overload the JVM with threads.  If it is a small tool used internally to
your company, don't worry too much about it.  If it is a webapp that
serves a high-volume web-site, check out ThreadPoolExecutor and the likes.

Whatever you decide to do, I *strongly* recommend you read the book Java
Concurrency in Practice.  It describes all the tools available to Java
programmers and most of the caveats of multi-threaded applications in
the Java platform.
<http://virtualinfinity.net/wordpress/technical-book-recommendations/java-concurr
ency-in-practice/>