Cathode Ray Tube. I won't go into it much, but basically it has a glass panel with phosphors on it, and shoots beams at the panel that cause the phospors to light up and generate colored light. This is what the really old TVs and monitors that were like a half meter thick were using. They are obsolete now and are not widely produced anymore.
Liquid Crystal Display. An LCD display has two parts, a transparent color filter (the LCD panel), and a light source behind it that shines through to illuminate it (the backlight). It's a stained glass sort of idea. The color filter is an array of tiny liquid crystals and it uses electrical currents to rotate them around, to bend and manipulate the light that passes through. There are many variations and versions of this technology. The backlight is always on and shines through the whole display, and cannot be blocked completely, so even when a part of the display is displaying black (where the crystals are rotated into a position that blocks the backlight from coming through), there is some light that bleeds through, giving it a white haze and relatively lower contrast than other types of TV. It is still quite good though. You may hear the term "TFT-LCD" which is just being more technical and specific, but you can basically ignore it, because all LCD TVs, monitors, phones, everything, they are all TFT-LCDs, people don't call it that anymore because it is implied. Non-TFT-LCDs are like... digital watches and microwave clocks and stuff like that.
The Backlight can be either:
CCFL (Cold Cathode Fluorescent Light). Original LCD TVs used this, there were no other types at the time so we just called them LCD TVs. Since it uses fluorescent lights, it takes some time to warm up before it can display at maximum brightness.
LED (referred to as LED or LED-LCD). More power efficient and thinner. Instant full brightness capability at power-on. Generally newer LCD TVs are this type. So to be clear, "LED" TVs are a variation of LCD TVs. LED and LCD TVs both use the same display technology (LCD), just a different lighting method. Almost all LED LCD monitors and all TVs use WLED (white LED) as the backlight, although you may encounter monitors using RGB LEDs or GB LEDs w/ red phosphor as the backlight, which gets rid of the white haze and is used for extreme color accuracy. These monitors are very expensive and are made for professionals that work with graphics and images where color accuracy is critical.
The LCD Panel which the light passes through, controls how it appears to the user, and it also has various types due to improvements and revisions over the years.
TN (Twisted Nematic) is a cheap generic type, inexpensive, but the colors wash out when viewed at an angle and the color reproduction is mediocre at best. TN can be found on budget computer monitors. It won't be found on TVs because the poor viewing angles make it almost useless. If a monitor does not specify what type of panel it has, it is using TN. If it uses an IPS or VA panel, that is a point of advertisement, and will be listed somewhere noticeable. Some of the very highest quality TN panels have respectable color reproduction, and are used in premium "gamer" monitors because TN can switch colors faster than IPS or VA, giving it slightly smoother looking motion. However, IPS is by no means "bad" for gaming as some people will tell you.
IPS (In-Plane Switching) uses an improved arrangement of the liquid crystals, and is a more common premium option, offering higher brightness, more vivid colors, deeper blacks than TN, and can be viewed from any angle without color shifts. IPS is usually the preferred panel type. High-end LCD TVs use these, for the wide viewing angles. There are a lot of sub-variants of IPS as manufacturers make small improvements, so you will see things like eIPS, E-IPS, AH-IPS, P-IPS, S-IPS, PLS, Super PLS... All just IPS with minor adjustments and refinements. All of them are good and they are all similar, so it's not worth paying much attention to.
VA (Vertical Alignment) is a less common display type, and it falls somewhat inbetween TN and IPS. It has much better colors than TN, but not as good as IPS, viewing angles almost as good as IPS, and very deep blacks, better than IPS. You may see "MVA" or "PVA" or "M-PVA" or "AMVA" monitors which are part of the VA family of panels. Similar story to the different IPS variants. Some people prefer VA panels over IPS for the deeper black capabilities. They can be found in TVs more commonly than in monitors.
OLED (organic LED) is a very new display type, with great potential but some problems that still need to be solved. OLED display technology is still in development. As opposed to LCD, which uses a color filter, and a single light source from behind to illuminate it, OLED displays just have a giant grid of individual colored LEDs for every pixel. Naturally, it is very expensive. Since each OLED is individually controllable, the OLEDs can be turned off completely when they need to display black. OLED displays have very deep black levels and excellent contrast (infinite contrast ratio, technically), as well as very vivid colors. Current implementations tend to have oversaturated colors, but that will be solved with time as the technology matures and color calibration and balance improves. OLEDs degrade in brightness over time. The different color OLEDs degrade at different rates, so over several years, the color balance will be skewed. Again, it is a developing technology, and research continues to be done to make more robust OLEDs that degrade slowly enough to not matter. Because it no longer has two parts like LCD TVs do, and don't need a backlight, OLED TVs can be made extremely thin, and even flexible, using the right materials. The power usage of OLED TVs varies wildly depending on what it is showing, if it is a dark scene where most of the OLEDs are off, the power is very very low, when it is showing white where all the OLEDs are active, it consumes 2 to 3 times the power of an LED LCD TV. You may hear about "AMOLED" displays which means Active Matrix OLED. This is just being redundant, because all OLED displays in TVs and monitors will be using an active matrix. Passive matrices don't scale well to higher resolutions so aren't used for displays. Similar to "TFT-LCD", you don't really need to put the "AM" in front of OLED because all OLED displays will be using an active matrix, so the "AM" is already implied, but vendors do it anyway to sound fancy.
Plasma TVs have an arrangement of small gas chambers behind a glass panel, each chamber contains some amount of a Noble gas. A grid of electronics behind the gas chambers applies voltage to different cells, which illuminates the Noble gas in that cell. Similar to OLED, each cell is independent of the others and can be simply off when it is supposed to show black, so Plasma TVs also have very excellent black levels. They also have very vibrant colors and wide viewing angles, and don't have any problems with motion blur like LCD-based displays might, however LCDs can generally achieve higher brightness. Most plasma displays also have glossy panels (due to the panel construction), so this combined with the lower brightness and deep blacks make plasma TVs ideal for dark rooms. Plasma TVs can be made fairly thin (though not quite as thin as LCD or OLED displays) but consume more power than LCD or OLED-type TVs, and the gas inside them gets hot after long usage, leading to problems with burn-in where a permanent afterimage is left behind and never fades if a static image stays on the display for a long period of time. Manufacturers have implemented various technologies and methods of mitigating burn-in as much as possible so it is not as much of an issue as before, although the problem is not totally gone.
So in conclusion, basically Plasma is Plasma, OLED is OLED, CRT is CRT, and everything else is some variant of LCD.