<!DOCTYPE html>
<html>
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script>
$(document).ready(function(){
$("input[type='checkbox']").change(function(){
if($(this).val()=="other")
{
$("#otherAnswer").show();
}
else
{
$("#otherAnswer").hide();
}
});
});
</script>
</head>
<body>
No <input type="checkbox" name="answer" checked="checked" value="no"/> <br><br>
Yes<input type="checkbox" name="answer" value="yes"/> <br><br>
Other <input type="checkbox" name="answer" value="other"/><br>
<input style="display:none;" type="text" name="otherAnswer" id="otherAnswer"/>
</body>
</html>
Run it yourself