Edit in JSFiddle

<div id="div1">
    <div id="div2"></div>
</div>

#div1 {
    width: 100%;
    height: 200px;
    border: 1px solid black;
}
#div2 {
    width: 100px;
    height: 100px;
    border: 1px solid blue;
    position: relative;
    top: 50%;
    left: 50%;
    transform: translate(-50%, -50%);
    -webkit-transform: translate(-50%, -50%);
}