If you have your CSS in an external file, then it's often convenient to display an image that's used frequently across the site (such as a header image) as a background image, because then you have the flexibility to change the image later.
For example, say you have the following HTML:
<div id="headerImage"></div>
...and CSS:
#headerImage {
width: 200px;
height: 100px;
background: url(Images/headerImage.png) no-repeat;
}
A few days later, you change the location of the image. All you have to do is update the CSS:
#headerImage {
width: 200px;
height: 100px;
background: url(../resources/images/headerImage.png) no-repeat;
}
Otherwise, you'd have to update the src attribute of the appropriate <img> tag in every HTML file (assuming you're not using a server-side scripting language or CMS to automate the process).
Also background images are useful if you don't want the user to be able to save the image (although I haven't ever needed to do this).