jQuery menu: hide and show on click
Some general style points:


Indentation, it's important. Please indent one level for each set of braces moving forward. 
Frivolous comments. You have one comment for each function. These comments simply repeat what the names of the functions already tell us. They're noise. Remove them. I find it's a good practice to write pseudocode comments and then "fill in the blanks", but they shouldn't stay once you've implemented it. Comments should always say why, rarely should they say what. 


Now we can see what's really going on a little better. 

function hideNav() {
    $('nav').hide();
}

hideNav();

function showNav() {
    $('nav').show();
}

$('button').click(function() {
    if($('nav').is(':hidden')){
        showNav();
        $(this).text('Close me');
    }
    else
        hideNav();

    if($('nav').is(':hidden')){
        $('button').text('Open me');
    }
});


Personally, I don't see a point to the showNav() and hideNav() functions. It seems they don't do much except save a few keystrokes, but you've already written them and they're not actually hurting anything. I guess they're ok. 

This else statement really needs some braces. 


    if($('nav').is(':hidden')){
        showNav();
        $(this).text('Close me');
    }
    else
        hideNav();

    if($('nav').is(':hidden')){
        $('button').text('Open me');
    }



It's really not clear when the second if($('nav').is(':hidden') is supposed to execute. I think it should look like this. 

    if($('nav').is(':hidden')){
        showNav();
        $(this).text('Close me');
    } else {
        hideNav();
    }

    if($('nav').is(':hidden')){
        $.('button').text('Open me');
    }


Which brings to mind some code duplication. I would create a isNavHidden() function to simplify all this a bit. 

function isNavHidden() {
    return $('nav').is(':hidden');
}


Then you could write the above snippet like this. 

    if(isNavHidden()){
        showNav();
        $(this).text('Close me');
    } else {
        hideNav();
    }

    if(isNavHidden){
        $.('button').text('Open me');
    }