First, this is the Premier Pro forum, not Premiere Elements.
Second, you have those bars because you shot in a 4:3 aspect ratio, and are trying to export to probably a 16:9 "widescreen" aspect ratio, which most cameras shoot these days.
You are using the wrong Project Settings for your project.
But in order to tell you what you can do about it, we'll need to know which version of the program you're using on what operating system.
We'll also need to know what resolution your camera is shooting at (1920x1080?) and if your camera is saving in MOV, AVI or MP4 format.
The OP gave the frame-size of the camera, 640x480, at least as far as he could tell. Which is why I'd asked for the screen-grabs showing the info that I'd asked for ... to confirm all of that data. Empirically.
Most likely, if that camcorder is storing video as MOVs, the project will need to be set up manually. (The user will also need to have Quicktime installed, per the program's system requirements.)
How to set the project settings depends on which version of the program the user is using.