Resolution means the number of pixels, or individual picture elements, a screen contains. The first number indicates the number of pixels going across the screen from left to right; the second, the number of pixels from the top of the screen to the bottom.
A 720p set displays 1024x768, 1280x720, or 1366x768 pixels. A set with 1080p resolution, sometimes advertised as "full HD," displays 1920x1080 pixels. Most new HDTVs with screens 40 inches and up have 1080p resolution.
Newer Ultra HD (UHD) models, which display 3840x2160 pixels, are sometimes called "4K" sets because they contain almost 4,000 horizontal pixels. The greater pixel density of UHD TVs—four times that of 1080p TVs—enables them to present even finer detail. Most UHD TVs are offered in larger 65- to 85-inch screen sizes, but you can also find UHD sets as small as 40 inches.
3D-capable UHD sets that use passive technolog can present full 1080p resolution to each eye, rather than reducing the vertical resolution below full HD resolution, as 1080p passive-3D sets do.
You will still pay a fairly hefty premium for a UHD model from a major brand, but prices are falling significantly and will continue to decline throughout next year. Most Ultra HD sets are LCD TVs with LED backlights, but there are now a few Ultra HD OLED models from LG, and more are expected.
The larger the TV screen, the more you can appreciate fine detail. That's one reason the first UHD sets have fairly big screens. With 1080p TVs, the fine detail is more noticeable on a 50-inch or larger TV, though you might see subtle improvements on a 40- to 47-inch screen, especially when viewed up close. In smaller sizes, the benefits of 1080p are less obvious.
One exception: If you plan to use your TV as a computer display, 1080p resolution is a plus even on smaller screens. The higher resolution will let you see more text and graphics onscreen with greater clarity and finer detail than you would on a 720p set. (You might have to connect your computer to the TV with an HDMI input to take full advantage of the 1080p resolution and to avoid cutting off outer edges of the image--otherwise known as overscan.)
However, resolution alone doesn't determine picture quality. Factors such as brightness, contrast, and color accuracy also come into play. What you're watching matters too.
Just remember that to fully exploit the potential of a 1080p TV, you need top-quality high-def content. You can get that from a Blu-ray disc, which contains true 1080p content. A 1080p set will convert HD signal formats (720p and 1080i signals from your cable box, for instance) to match its native screen resolution. If the video quality of the programming is good and the TV does the job well, the picture can be outstanding.