Use localStorage().

Local storage is per origin (per domain and protocol)

• On click of DIV close, you can get the current time-stamp
• Add number of hours (24) to that time-stamp
• Store that value in localStorage as localStorage.setItem('desiredTime', time)
• Check current time-stamp with that stored time-stamp localStorage.getItem('desiredTime'), based on that show/hide

jQuery

$(document).ready(function(){
        //Get current time
        var currentTime = new Date().getTime();
        //Add hours function
        Date.prototype.addHours = function(h) {    
           this.setTime(this.getTime() + (h*60*60*1000)); 
           return this;   
        }
        //Get time after 24 hours
        var after24 = new Date().addHours(10).getTime();
        //Hide div click
        $('.hide24').click(function(){
            //Hide div
            $(this).hide();
            //Set desired time till you want to hide that div
            localStorage.setItem('desiredTime', after24); 
        });
        //If desired time >= currentTime, based on that HIDE / SHOW
        if(localStorage.getItem('desiredTime') >= currentTime)
        {
            $('.hide24').hide();
        }
        else
        {
            $('.hide24').show();
        }
});

HTML

<div>DIV-1</div>
<div class='hide24'>DIV-2</div>

Things to note

• You can use $.cookie as well, but that's an older approach now.
• <div> with class hide24 will be hidden only.
• Make sure that you put this code in general JavaScript, which loads on every HTTP request of your website.
• For localStorage, you should have HTML5 browsers.

Web Storage HTML5

Hope this helps.