这应该是你想要的答案，重新优化了一下。

var timeoutObj = null;
$("#append").on("mouseenter mouseleave","p",function(e){
    if(e.type == "mouseenter"){
        //鼠标进入
        (function(me){            
            timeoutObj = setTimeout(function(){
                $(me).text("wow");
            },3000);     
        }(this));           
    }else if(e.type == "mouseleave"){
        //鼠标离开        
        $(this).text("amaze");
        if(timeoutObj != null){
            clearTimeout(timeoutObj);
        }
    }
});

settimeout(functoin(){},3000)

<script type="text/javascript">
    $("#append").on("mouseenter mouseleave","p",function(e){
                if(e.type == "mouseenter"){
                    //鼠标进入
                    $(this).text("wow");
                    setTimeout("Onlive()",3000);
                }else if(e.type == "mouseleave"){
                    //鼠标离开
                   $(this).text("amaze");
                }
    });
    function Onlive(){
        alert("3秒弹出");
    }
</script>