To have a text box (or image :happy_tb: ) displayed on top of each page (apart from posts in single post view) but above header I have added following piece of code to index.php, page.php and archives.php just bellow <div id="content"> [that’s div which starts content of the page]:

<div id="introtext">
<?php echo ‘This message is supposed to show up just under header on each page’; ?></div>

Then I have added to style.css:
#introtext {
padding: 5px;
margin: 10px 3px 0 3px;
background-color: #990000;
color: #ffffff;
text-align: center;
clear: both;
}
I’ve used clear:both; to make sure sidebar won’t drop down the page.
And that’s final result :).
introtext
(click on image to enlarge)