Shuryga,
<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<style>
.small-block
{
position: relative;
width: 30px;
height: 30px;
background-color: Green;
border: 1px solid black;
}
.small-block:hover
{
background-color: lightgreen;
}
</style>
<script>
$(function () {
var mess = ['Первый', 'Второй', 'Третий'];
var timeout;
$('.small-block').each(function (indx, element) {
$(element).on('mouseenter', function () {
clearTimeout(timeout);
timeout = setTimeout(function () {
$('.big-two').html(mess[indx]);
}, 1000);
})
})
})
</script>
</head>
<body>
<div class='big-one'>
<div class='small-block'></div>
<div class='small-block'></div>
<div class='small-block'></div>
</div>
<div class='big-two'>
</div>
</body>
</html>