What does the 'static' keyword do in a class?

static members belong to the class instead of a specific instance.

It means that only one instance of a static field exists^[1] even if you create a million instances of the class or you don't create any. It will be shared by all instances.

Since static methods also do not belong to a specific instance, they can't refer to instance members. In the example given, main does not know which instance of the Hello class (and therefore which instance of the Clock class) it should refer to. static members can only refer to static members. Instance members can, of course access static members.

Side note: Of course, static members can access instance members through an object reference.

Example:

public class Example {
    private static boolean staticField;
    private boolean instanceField;
    public static void main(String[] args) {
        // a static method can access static fields
        staticField = true;

        // a static method can access instance fields through an object reference
        Example instance = new Example();
        instance.instanceField = true;
    }

[1]: Depending on the runtime characteristics, it can be one per ClassLoader or AppDomain or thread, but that is beside the point.

It means that there is only one instance of "clock" in Hello, not one per each separate instance of the "Hello" class, or more-so, it means that there will be one commonly shared "clock" reference among all instances of the "Hello" class.

So if you were to do a "new Hello" anywhere in your code: A- in the first scenario (before the change, without using "static"), it would make a new clock every time a "new Hello" is called, but B- in the second scenario (after the change, using "static"), every "new Hello" instance would still share and use the initial and same "clock" reference first created.

Unless you needed "clock" somewhere outside of main, this would work just as well:

package hello;
public class Hello
{
    public static void main(String args[])
    {
      Clock clock=new Clock();
      clock.sayTime();    
    }
}

The static keyword means that something (a field, method or nested class) is related to the type rather than any particular instance of the type. So for example, one calls Math.sin(...) without any instance of the Math class, and indeed you can't create an instance of the Math class.

For more information, see the relevant bit of Oracle's Java Tutorial.

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Sidenote

Java unfortunately allows you to access static members as if they were instance members, e.g.

// Bad code!
Thread.currentThread().sleep(5000);
someOtherThread.sleep(5000);

That makes it look as if sleep is an instance method, but it's actually a static method - it always makes the current thread sleep. It's better practice to make this clear in the calling code:

// Clearer
Thread.sleep(5000);