A DTV converter box is a tuner that converts a signal from digital to analog, so that a digital television (DTV) transmission can be used with an analog TV set. HDTVs do not require converter boxes, so if your set is old enough to require one, you might as well consider upgrading.
Since analog TV sets are no longer being manufactured, the only reason you would need a converter box is if you have a very old TV that only accepts analog signals. All analog TV broadcasting stopped in the US in 2009, so if you want to watch HD TV on your old analog set, you will need to purchase a DTV converter box.
All HDTVs are built to handle digital transmissions. In fact, connecting a DTV converter box to your HDTV will degrade the picture quality. If you have an HDTV, you only need a converter box if you want to connect an analog VCR.