In Word 2007 (I've forgotten if it's the case for Word 2003), you can select
existing text, then click Draw Text Box (click Insert ribbon tab, Text Box,
Draw Text Box), and Word places a text box around the selected text.
You can also cut & paste existing text into a text box.
But, it does sound as if the text box is covering up text rather than
containing it in the current case. This would happen if text is not selected
when you choose Draw Text Box, and you attempt to draw a box around existing
text--the result is an empty text box that covers up existing text
(depending on the Wrapping type that is used). As logical as that action
might seem, it's not how the feature works in Word.