Show div when hover another div using only css

This will work, but only if the two divs are adjacent and b follows a.

#a:hover + #b {
    background: #f00
}

<div id="a">Div A</div>
<div id="b">Div B</div>

If you have divs in between use ~

#a:hover ~ #b {
    background: #f00
}

<div id="a">Div A</div>
<div id="c">Div C</div>
<div id="b">Div B</div>

To go the other way around, unfortunately you will need Javascript

// Pure Javascript
document.getElementById('b').onmouseover = function(){
    document.getElementById('a').style.backgroundColor = '#f00';
}
document.getElementById('b').onmouseout = function(){
    document.getElementById('a').style.backgroundColor = '';
}

// jQuery
$('#b').hover(
  function(){$('#a').css('background', '#F00')}, 
  function(){$('#a').css('background', '')}
);

Full fiddle http://jsfiddle.net/p7hLL/5/

If you don't want to use the selector + or ~ which aren't compatible with some browsers, it is just possible if the <div /> to show (e.g. div#b) is a child of the <div /> to hover (e.g. div#a).

<div id="a">
    <div id="b"></div>
</div>

<style>
    div#b {
        display: none;
    }

    div#a:hover div#b {
        display: block;
    }
</style>