1080p/1080i + 720p/720i - I'm going to breeze right over this one. A higher number means a more detailed, sharper image. "p" stands for progressive scan, and "i" stands for interlaced. Progressive scan is better than interlaced in terms of visual quality. If you want a more detailed explanation, you can find one here.
Contrast Ratio/Dynamic Contrast Ratio - Contrast ratio is basically a measurement of the range between the lightest and darkest colors displayed on the screen. The larger the ratio, the brighter the brights, the darker the darks. If what your are reading says simply "Contrast Ratio" without "Dynamic", they mean the ratio of just what's capable of being displayed at the same time on screen. Dynamic Contrast Ratio is used to describe televisions where the entire screen adjusts its brightness level, and compares the darkest possible black to the brightest possible white, but those two will never be visible at the same time.
What it means to you: A fixed contrast ratio is the easier to interpret. Small numbers mean that the image on the screen will look a little faded or washed out. Blacks will glow or appear dark grey. Large numbers mean more realistic images, with truer colors. Dynamic contrast ratios really mean nothing to you as a consumer, and manufacturers will not post the meaningful ratios on the outside if they have Dynamic Contrast Ratio listed. They are intended to sound impressive without actually meaning anything about quality(like megapixels when buying a camera). You could ask to see the manuals, or you could simply just look at the display and form your own opinion of the image quality. Look at the black areas on the images, if they are dark enough for you and you can still make out everything else on the screen, that's all you really need. Ignore the numbers.
NTSC/ATSC
NTSC is the "old" analog tv signals that just disappeared from the airways, but are still being sent to your non-HD TV's from the cable/satellite companies. ATSC is the new digital signal. Any HD TV will definitely accept ATSC, and should certainly still accept NTSC, which is important if you don't plan on abandoning your VCR or DVD player anytime soon. Chances are very good that you won't need to be concerned with this for a few more years at least, as it is standard for HD TV's to accept both signals. If you are planning on buying a TV Tuner for your computer, however, you will need to remember this.
HDMI/Component/DVI
These are the commonly accepted inputs for transferring an HD signal to your TV. The main distinction here is that HDMI also sends audio across the same cable, while Component and DVI transmit only video. Technically, component is made up of 3 cables(red, green, and blue) plus whatever audio cables you need(usually the red and white RCA cables), but they tend to sell these as a single cable. There are differences in the video quality across these different cables, but if you are starting off with this guide, chances are good that any of the three would be perfect for you.
-Coax/Composite
These are the old standards of cables for your Standard Definition TV's. Any HD TV will have at least 1 coax(the round, black cord with a single pin in the middle that needs to be screwed in), and many include composite(the red, white and yellow plugs). Having these will be important if you plan on hooking up anything that's not brand new, such as a VCR, DVD player that's a few years old, or any video game consoles from more than a couple years ago. If you have your cable plugged into your HD TV via coax, there are some things to note, which I've mentioned below.
Plasma/LCD(+LED)/DLP/(AM)OLED
The two most common types of HD TV are Plasma and LCD. Plasma's will generally have better contrast ratios and truer motion than LCD and tend to cost more as a result. To address some of the pitfalls of LCD(poor contrast ratios, motion and brightness) some manufacturers are adding Light-Emitting-Diodes to the LCD TV's as a backlight which helps address some of these issues. Pricing for these generally falls between standard LCD's and Plasmas and so does the image quality. These may be marketed only as "LED" TV's but in truth, they are still LCD's, just enhanced. If you are looking for a large TV, 50 inches or larger, DLP is another option. These will not be TV's that you mount to you wall, but rather take up some floor space. They tend to be cheaper than plasmas in the same range, and have a good-quality image. At the time of writing this, any TV with "OLED" in the description is too expensive for anyone, this includes "AMOLED" as well. If future years, they may be priced more reasonably, and I may revisit this topic and speak more on them then.
Noteworthy:
-Garbage in: Garbage out - Unless you have an entirely HD package through your cable or satellite service, you will notice that some channels look horrible on your new TV. They might not be broadcast in HD, so the image quality will be poorer by comparison to everything else. Likewise, if you use coax(the screw on cable) or composite(red, white, yellow) as your inputs, the image quality will not be HD. It's no fault of the TV in these cases, it's just something that you will notice and have to accept with the purchase of your HD TV.
-Network features(Netflix/Youtube/Amazon + Media Extenders) - A number of new TV's have some added features that make use of your internet connection. If you are a Netflix subscriber, you may already be aware of their Watch Instantly feature, where you can watch their movies through their website without the DVD's. Some TV's(and Blu-Ray players) allow you to view your Watch Instantly Queue through the TV, so if you use Netflix, or were planning to, this might be a feature that is worth consideration. In addition to Netflix streaming, many models include access to YouTube or even Amazon's online movie rental service. If that appeals to you, you have some options to look for in your TV purchase. Others allow you to access videos that you may have on your computer through the network. Chances are good that setting up that feature will be a fairly intensive process, so don't expect the world of that feature unless you're willing to put in some significant legwork.
-Upscaling/Upconverting - This is a good feature to look for if you want to get some extra life out of your non-HD gadgets that are hooked up to your TV. This is the process of improving an SD signal to an approximation of an HD signal. It won't look as good as a true HD signal, but it will look better than a non-upscaled SD signal, and for many, that's good enough.
-Refresh Rates - This is simply how many times in 1 second the screen can change the image being displayed. This is important especially on LCD TV's as they can tend to have a ghosting effect, where an image fades away when it should simply disappear instantly. A high refresh
rate will eliminate or greatly reduce the ghosting effect found on
LCD's. Plasma TV's don't usually have a problem with ghosting, so their
refresh rates are not typically advertised.