The first respondent stated:
"The resolution you are talking about is width by height. You can have a display that is 1024x768 that is <720p, 720p, or 1080p."
This is not accurate. This is why.
For the last few years we have heard the numbers 720 and 1080 used frequently when discussing high definition images. But what do those numbers mean? Well, those numbers represent the number of rows of pixels that make up the display or image. An "HD 720" display has 720 rows of pixels available and happens to have 1,280 columns of pixels. An "HD 1080" display has 1,080 rows of pixels with 1,920 columns. As you see, there are more columns than rows. This is what makes the image wider than tall. Both HD 720 and HD 1080 are 16:9 ratio.
A 1024 x 768 resolution happens to be a computer resolution. This resolution is called XGA and happens to be a 4:3 ratio as opposed to the 6:19 ratio you get with 720 and 1080.
Having said this, let's look at how an HD 720 image will fit within a 1024 x 768 display.
Of course the 720 rows of pixels found in the image will fit within the 768 rows the display is capable of producing. But the 1,280 columns of pixels of an HD 720 image will obviously not fit within the 1024 columns the display is capable of producing.
This means that 256 columns of pixels (128 columns on each side of the HD 720 image) will be cropped off the image to fit onto the 1024 x 768 display. Either that, or the pixel density can be adjusted so that the HD 720 image can image can fit. But unfortunately, by doing so, you no longer have a true HD 720 image and this is where you get the black lines on the top and bottom of the screen known as letter boxing.
PsychologyGuy also said...
"that is more of an issue with the fact that most things (even brand spankin new LCD/LED televisions) don't utilize precise 16:9 aspect ratios. For example, I have a Samsung 6 series widescreen LCD TV that still has the banding on 16:9 movies."
This is also not true. If you do the math, HD 720 and HD 1080 are both precisely 16:9 ratios. The reason why his TV still has the letter boxing (black bands on top and bottom) is because movies are not filmed in 16:9 ratio, but instead a 2.40:1 ratio is used.
When displaying a 2.40:1 ratio image (which is more than twice as wide as the hight of the image) on a 16:9 display (which has a width less than double the height) the picture must be shown in letterbox format in order to prevent picture distortion or cropping.