.html()
only takes a string OR a function as an argument, not both. Try this:
$("#showDiv").click(function () {
$('#theDiv').show(1000, function () {
setTimeout(function () {
$('#theDiv').html(function () {
setTimeout(function () {
$('#theDiv').html('Here is some replacement text');
}, 0);
setTimeout(function () {
$('#theDiv').html('More replacement text goes here');
}, 2500);
});
}, 2500);
});
}); //click function ends