In video and television, the lower third refers to the lower portion of the frame which contains graphical information such as station ID, name/title keys, etc.
In a talking head shot like the one pictured here, the lower third graphics sit somewhere below the presenter's shoulders.
In most cases the graphics don't actually take up a full third of the picture. If the only requirement is a name/title key, not much space needs to be used. On the other hand, for programs which need to include a lot of information, the full third may not be enough and a side panel is added.
If you have the right image editing software, making your own lower thirds is quite easy. See Creating Lower Thirds.
You can also buy pre-made lower thirds from many places on the Internet. These come in common formats which you can import into your project and add text or other images as necessary. Pre-made lower thirds can be anything from a basic background to a complete template.
Note: Animated lower thirds add impact, as long as they are done tastefully. Don't over-animate your graphics to the point of being distracting. A good compromise is to animate new text or images as they arrive on screen and then let them sit still.