Digital is digital vs analog. Analog would use things like radio waves (more or less) to transmit the image/signal/data. Digital uses 0's and 1's. Its like moving information around on a computer, this information just happens to be your TV programming. So digital, in theory, provides a stronger, more consistent signal/image.
HD is HD vs SD. This has to do with resolutions. SD is 720x486 in resolution and 4:3 in aspect ratio. HD is either 1280x720 or 1920x1080 in resolution and 16:9 in aspect ratio (both resolutions).
To get HD you must have an antenna, cable box, or satellite box that can transmit HD signals. Then you can turn your TV to an HD channel and get HD. All major networks right now have both HD and SD channels. So say NBC is channel 15 for you, that's NBC SD. NBC HD would be something like perhaps channel 207. So you need an HD capable box to allow you to see that HD channel properly.
Alternatively, you can watch HD with a BluRay player. But this is for watching BluRay discs or DVD discs (which are up converted) in HD. So you're watching discs here, not broadcast TV. A BluRay player won't unlock broadcast TV channels for you.