An HDTV receiver, also know as an HDTV tuner, is best thought of as the method by which what used to be called "HDTV ready" televisions, now called HDTV monitors, can access off-air HDTV signals.
If you want to view one of the many HDTV channels now broadcast over the air in the US, and you don't have an HDTV set with an integrated HDTV tuner, you'll need an HDTV receiver. You'll also need an HDTV monitor, which connects to the receiver via either a DVI or HDMI cable.
If you have an old external antenna you may need to upgrade it and if you use an internal, set-top antenna you may want to get one specifically designed for HDTV.
While it is still possible to buy an HDTV receiver specifically for the purpose of watching off-air HDTV programming, the rapid rise in HDTV availablity through services like Voom and DirecTV, and the increase in the number of available integrated HDTV sets means that it's now more common to find an HDTV tuner combined with a DirecTV satellite receiver in one box, or with an LCD TV or plasma TV.
It's also now possible to buy an HDTV tuner for your PC. The ATI HDTV All in Wonder PCI card allows you to view and record off-air HDTV programming on your PC. HDTV PC cards are also available from AccessDV and DVICO.
If you're a Mac user, you can get an HDTV receiver in the form of El Gato's EyeTV 500. The EyeTV 500 connects to the Mac via FireWire and is able to receive over-the-air HDTV broadcasts. You can view the broadcasts on your Mac and record them on your hard drive.
To view HDTV in the highest possible quality from a PC or Mac, you should have an LCD display which connects to your computer via a Digital Video Interface (DVI). That way the whole signal is digital and no analog conversion is required.
Whatever type of receiver you decide to buy, you should read HDTV reviews before making a decision.