Edit in JSFiddle

$(function(){
    $('#btn').on('click', function(){
        $('#result').val(h($('#txt').val()));
    })
});
function h(str) {
    str = str.replace(/&/g,"&") ;
    str = str.replace(/"/g,""") ;
    str = str.replace(/'/g,"'") ;
    str = str.replace(/</g,"&lt;") ;
    str = str.replace(/>/g,"&gt;") ;
    return str ;
} 

<div>
    <textarea id="txt" cols="50" rows="5"></textarea><br />
    <textarea id="result" cols="50" rows="5"  readonly="readonly"></textarea><br />
    <input id="btn" type="button" value="エスケープ！" /><br />
</div>