User113716's great answer will no longer work in jQuery 1.9+, because the pseudo-event hover is no longer supported (upgrade guide).

Also since jQuery 3.0 delegate() for binding events is officially deprecated, so please use the new on()^(docs) for all event binding purposes.

You can easily migrate user113716's solution by replacing hover with mouseenter mouseleave and switching to the on() syntax:

$('mydiv').on('mouseenter mouseleave', 'seconddiv', function(event) {
    $(this).toggle( event.type === 'mouseenter' );  
});

If your problem is more complex than a simple toggle, I suggest binding two separate events:

$('mydiv').on('mouseenter', 'seconddiv', function( event ) {
    // do something
}).on('mouseleave', 'seconddiv', function( event ) {
    // do something different
});

NB: Since hover was removed in v1.9 and on() was introduced in v1.7, there is no real need for a solution using delegate() - but if you like it for some reason; it is still there (for now) and does the job:

$('mydiv').delegate('seconddiv','mouseenter mouseleave', function(event) {
    $(this).toggle( event.type === 'mouseenter' );  
});

With delegate()^(docs) , you assign it to a container, and the first argument is the element that should trigger the event.

Also, .delegate() accepts only one function, so for the hover event you need to test the event.type to determine show()^(docs) or hide()^(docs) .

$('.someContainer').delegate('.someTarget','hover', function( event ) {
    if( event.type === 'mouseenter' )  
        $('seconddiv').show();  
    else
        $('seconddiv').hide();  
});

For show/hide, a shorter way to write this is to use toggle()^(docs), which can accept a switch argument where true means show and false means hide:

$('.someContainer').delegate('.someTarget','hover', function( event ) {
    $('seconddiv').toggle( event.type === 'mouseenter' );  
});

Note that the mouseenter event is reported as of jQuery 1.4.3. If you're using 1.4.2, it will be reported as mouseover.

---

EDIT:

If I'm understanding your comments below, you'd have something like this (using the proper selectors of course).

$('mydiv').delegate('seconddiv','hover', function( event ) {
    $(this).toggle( event.type === 'mouseenter' );  
});

I know the OP wanted a delegate solution (so was I when I bumped into this question...)

But after further investigation I found out its possible to achieve the same without js/jquery code at all

All you need is a bit of CSS

.someContainer .seconddiv{
    display : none;
}

.someContainer:hover .seconddiv{
    display : block;
}

INMO it a much more efficient/ligthwheigth solution