еще один вариант:
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<script>
$(document).on('ready', function() {
$(".seachitem").hide();
$('input.search').keyup(function(){
$(".seachitem").hide();
$(".seachitem:contains(" + $(this).val().toLowerCase() + ")").show();
});
});
</script>
</head>
<body>
<div class="seachbox">
<input type="text" class="search">
<p class="seachitem" style="display: block;">нг</p>
<p class="seachitem" style="display: block;">подарки</p>
<p class="seachitem" style="display: block;">белый</p>
<p class="seachitem" style="display: block;">ёлка</p>
<p class="seachitem" style="display: block;">шишка</p>
<p class="seachitem" style="display: block;">цветы</p>
<p class="seachitem" style="display: block;">горшок</p>
<p class="seachitem" style="display: block;">стул</p>
<p class="seachitem" style="display: block;">прованс</p>
<p class="seachitem" style="display: block;">обои</p>
<p class="seachitem" style="display: block;">зелень</p>
<p class="seachitem" style="display: block;">овечка</p>
<p class="seachitem" style="display: block;">кот</p>
<p class="seachitem" style="display: block;">камень</p>
<p class="seachitem" style="display: block;">природный</p>
<p class="seachitem" style="display: block;">девушка</p>
<p class="seachitem" style="display: block;">комод</p>
<p class="seachitem" style="display: block;">темно</p>
<p class="seachitem" style="display: block;">граффити</p>
<p class="seachitem" style="display: block;">светильник</p>
<p class="seachitem" style="display: block;">зима</p>
<p class="seachitem" style="display: block;">подушка</p>
<p class="seachitem" style="display: block;">кухня</p>
<p class="seachitem" style="display: block;">город</p>
<p class="seachitem" style="display: block;">свечи</p>
<p class="seachitem" style="display: block;">дети</p>
<p class="seachitem" style="display: block;">комната</p>
</div>
</body>
</html>