Nettuts has a screencast just to explain this: Quick Tip: The Difference Between Live() and Delegate()
Quote from the site:
// Live(), introduced in 1.3, allows for the binding
// of event handlers to all elements that match a
// selector, including those created in the future.
// It does this by attaching the handler to the document.
// Unfortunately, it does not work well with chaining.
// Don't expect to chain live() after calls like
// children().next()...etc.
$("li").live("click", function() {
$(this).parent().append("<li>New Element</li>");
});
// Delegate, new to version 1.4, perhaps should have been a complete
// replacement for Live(). However, that obviously
// would have broken a lot of code! Nonetheless,
// delegate remedies many of the short-comings
// found in live(). It attaches the event handler
// directly to the context, rather than the document.
// It also doesn't suffer from the chaining issues
// that live does. There are many performance benefits
// to using this method over live().
$('#items').delegate('li', 'click', function() {
$(this).parent().append('<li>New Element</li>');
});