The easiest way to do this is with your /includes/templates/your_template/css/stylesheet.css.
Find the id of the desired sidebox heading and set it to not display, e.g. add a new declaration to your stylesheet
Code:
#categoriesHeading {
display: none;
}
which will completely disable the categories heading text and its background block.
The lowest-tech way to find the id is with View Source:
<h3 class="leftBoxHeading" id="categoriesHeading">Categories</h3>
A very efficient way is with the Firefox Web Developer extension (download free from mozilla) and its Information > Display Element Information button.