Edit in JSFiddle

var maxTime = 1000,
    // allow movement if < 1000 ms (1 sec)
    maxDistance = 50,
    // swipe movement of 50 pixels triggers the swipe
    target = $('#box'),
    startX = 0,
    startTime = 0,
    touch = "ontouchend" in document,
    startEvent = (touch) ? 'touchstart' : 'mousedown',
    moveEvent = (touch) ? 'touchmove' : 'mousemove',
    endEvent = (touch) ? 'touchend' : 'mouseup';

target.bind(startEvent, function(e) {
    // prevent image drag (Firefox)
    e.preventDefault();
    startTime = e.timeStamp;
    startX = e.originalEvent.touches ? e.originalEvent.touches[0].pageX : e.pageX;
}).bind(endEvent, function(e) {
    startTime = 0;
    startX = 0;
}).bind(moveEvent, function(e) {
    e.preventDefault();
    var currentX = e.originalEvent.touches ? e.originalEvent.touches[0].pageX : e.pageX,
        currentDistance = (startX === 0) ? 0 : Math.abs(currentX - startX),
        // allow if movement < 1 sec
        currentTime = e.timeStamp;
    if (startTime !== 0 && currentTime - startTime < maxTime && currentDistance > maxDistance) {
        if (currentX < startX) {
            // swipe left code here
            target.find('h1').html('Swipe Left').fadeIn();
            setTimeout(function() {
                target.find('h1').fadeOut();
            }, 1000);
        }
        if (currentX > startX) {
            // swipe right code here
            target.find('h1').html('Swipe Right').fadeIn();
            setTimeout(function() {
                target.find('h1').fadeOut();
            }, 1000);
        }
        startTime = 0;
        startX = 0;
    }
});

<h1>Swipe Inside the Box</h1>
<div id="box"><h1></h1></div>

h1 {
    text-align: center;
    font-size: 24px;
}
#box {
    width: 300px;
    height: 200px;
    background: #eef;
    margin: 30px auto;
}
#box h1 {
    padding-top: 80px;
}