OLED's, are they better?
OLED's are great, but ofcourse that is subjective.
What is OLED, exactly?
OLED stands for Organic LED (Light Emitting Diode).
Succeeding the CRT, all monitors consist of a 2D array or Red, Green & Blue LED's per pixel. Traditionally there would be a backlight, nowdays using a white LED though before that it was a Cold Cathode Fluorescent Lamp (CCFL), a very small (about 1.5mm round) Fluoro Tube (and I have replaced those in the past). This backlight would generally sit right at the bottom of the screen beneath the bottom bezel (plastic monitor shroud/border), thats why the bottom is generally larger than the sides and top. Beneath the monitor panel (the LED Array) is a reflector layer that would take the light from the Backlight and evenly disperse it through the LED Array producing a visible image onscreen. Note that black displayed on screen is actually the RGB LED's working overtime to block the Backlight from coming through, that why under the right conditions (ie a dark room) you can see some light at the edges of the screen, between the bezel and panel, this is known as Backlight Bleed.
Note lastly that there is also HDR Backlighting technology that is sometimes used which omits the reflector in the previous sence and provides patches of adjustable backlights behind the RGB LED Array.
Great Backstory! but whats OLED?
Well, in the early days of OLED there was confusion that Organic stood for being made from non-synthetic products but Organic actually means they produce there own light and do not require nor have any reason to use the previously mentioned Backlight.
Is OLED Commonplace?
No but if your an iPhone user then starting with the iPhone X (10) Apple introduced OLED's to their display (though not iPad) indefinitely and most high end Samsung's and other Android phone's do aswell.
Is NanoLED, QLED, etc OLED?
No there not, currently only some Television's, a small amount of Computer Monitors and some Laptops specifically marked 'OLED' are. This means that in one form or another if its not marked 'OLED' its Backlit.
Why would anyone want an OLED?
Mainly, because its less of a light shining directly into the user's eye and less of a diffused bright white light in general.
Though there are other reasons such as deeper blacks (absent of light bleeding), less battery use (as only light required is used), serendipitously faster responce time (which reduces a phenomenon known as Ghosting, fast moving images appear to have a trail) and generally produce a very clear, vibrant & pure image.
Nonetheless OLED's being better or even required is thouroghly subjective and can be alot more expensive and for some people this cost can by all means be 'unjustified'.
Though they are very popular in the high end tech community (such as JaysTwoCents, LinusTechTips both swearing by them) and I personally wont buy anything else unless I cant avoid it.