Expanding on the information provided by @KennyTM:

• Internet Explorer (IE)
  • Engine: Trident
  • CSS-prefix: -ms
• Microsoft Edge
  • Engine: EdgeHTML → Blink³
  • CSS-prefix: -ms
• Mozilla Firefox
  • Engine: Gecko
  • CSS-prefix: -moz
• Opera
  • Engine: Presto → Blink¹
  • CSS-prefix: -o (Presto) and -webkit (Blink)
• Apple Safari
  • Engine: WebKit
  • CSS-prefix: -webkit
• Google Chrome
  • Engine: WebKit → Blink²
  • CSS-prefix: -webkit

¹⁾ Opera (version 15+) transitioned from Presto to WebKit-based Blink engine on February 12, 2013.

²⁾ Google (Chrome version 28+) adopted the WebKit-based Blink engine on April 3, 2013.

³⁾ Microsoft (Microsoft Edge 79+ stable) announced the switch to WebKit-based Blink engine for Edge on December 6, 2018.

WebKit acts as the web browser rendering engine for popular browsers such as Safari and Chrome.

The use of the -webkit prefix with CSS selectors signifies properties that are specifically meant to be processed by this particular engine, similar to how -moz properties function. Many developers are hopeful that these unique prefixes will eventually be replaced by standard properties like border-radius, eliminating the need for multiple rules targeting the same feature across different browsers. This situation arises from early "pre-specification" features designed not to disrupt compatibility once standardization occurs.

Just a quick update:...it's worth noting that this is unrelated to Internet Explorer, which actually utilizes a different rendering engine known as Trident.

This question has already been answered and accepted. However, for those still curious about why things seem a bit chaotic today, check out this informative article:

http://example.com/why-things-are-messed-up-today

It delves into the evolution of major rendering engines like gecko, webkit, and others, shedding light on how user-agent strings became so convoluted.

To summarize for those with limited time:

Enter Google's Chrome - which utilized WebKit, resembled Safari, and consequently requested pages designed for Safari. This led to a chain reaction where Chrome masqueraded as Safari, WebKit emulated KHTML, KHTML imitated Gecko, and all browsers claimed to be Mozilla. In the end, user-agent strings were a tangled mess, rendering them largely useless as everyone impersonated everyone else, causing widespread confusion.

-webkit- is like a special club that includes Chrome, Safari, Opera, and iOS browsers. They all share a common ancestor, so their capabilities and limitations when it comes to CSS and Javascript are often similar.

When a developer uses -webkit- followed by some code, it means that the code will only work on Chrome, Safari, Opera, and iOS browsers. Here is a breakdown:

-webkit- (Chrome, Safari, newer versions of Opera, almost all iOS browsers including Firefox for iOS)

-moz- (Firefox)

-o- (Older, pre-WebKit versions of Opera)

-ms- (Internet Explorer and Microsoft Edge)

The burning question remains... Does IE support WebKit?

Well, sort of. You can explore Chrome Frame, which acts as a plugin for Internet Explorer to utilize the Webkit engine. The downside is that convincing your site visitors to install the plugin may be a hurdle.

Update

It's important to note that Chrome Frame is no longer kept up-to-date or officially supported...

WebKit is a powerful layout engine specifically designed for web browsers to effectively display web content. It offers a variety of classes to showcase web content within windows, enabling features such as navigating links, managing browsing history, and tracking recently visited pages.

Originally developed from KHTML for Apple's Safari browser, WebKit has since expanded its reach to other platforms and is now a core component of Google's Chrome Browser.

The components of WebKit like WebCore and JavaScriptCore are made available under the GNU Lesser General Public License, while the remaining parts of WebKit operate under a BSD-style license.

Source Wikipedia

For more in-depth information on layout engines, please visit this link.

Webkit serves as the HTML rendering engine for popular browsers like Chrome and Safari.

This engine provides extensive support for various custom CSS properties which require the -webkit- prefix.

WebKit serves as the rendering engine for both Apple's Safari browser and Google's Chrome, distinguishing itself with CSS values prefixed by -webkit- that are specific to WebKit implementations, often incorporating non-standard features like CSS3.

In response to update 2: The W3C plays a crucial role in establishing standards for web technologies, providing guidelines that software developers use to create rendering engines. When adhering to W3C rules regarding elements like DIVs, engine writers ensure consistent behavior across browsers, whereas deviations may lead to compatibility issues.

Webkit serves as the backbone for rendering websites in browsers such as Safari and Chrome, among various others.

In my experience as a website designer, I often encounter the challenge of dealing with users who still use IE6+. While it's not usually a big issue, working with CSS becomes trickier because I have to incorporate multiple rendering syntaxes to accommodate each browser's requirements. It would be highly beneficial to have a universal CSS rendering system that is just as compatible with IE as it is with Chrome, Firefox, Opera, and other webkit browsers.

The tricky part about IE is that if I don't implement all the necessary CSS styles and renderings correctly, my websites may appear and function perfectly on every browser except for IE. This can lead to frustration among loyal IE users who expect a seamless online experience.

For instance, when I want to create a 1px grey border with a 10% border-radius, I can easily achieve this effect using the webkit property for Chrome and other modern browsers. However, for IE, I have to resort to separate CSS styles using traditional values like "border: 1px solid #E5E5E5" and "border-radius: 10%". While this workaround doesn't always guarantee consistent results across all versions of IE, it generally works well enough for myself and many others in the industry.

While this post may be on the older side, there is an alternative approach to rendering for outdated versions of Internet Explorer. Instead of relying solely on -webkit as a CSS Vendor Prefix, you can also integrate various JS applications by placing them towards the end of the HTML's HEAD.

Consider incorporating Modernizr, HTML5 Shiv, and Respond.js into your codebase. These IE-compatible polyfill scripts offer support for HTML5 elements in IE9 and earlier, utilizing polyfills and other essential resources to enhance rendering capabilities.

To implement these polyfills, simply apply HTML boolean logic to include them if the browser version is below a specified IE threshold. Here's an example snippet:

<head>
<!-- HEAD Elements -->  
<script src="path/to/modernizr.js" type="text/javascript"></script>
<!--[if lt IE 6]>
  <script src="path/to/HTMLSiv.js" type="text/javascript">
  </script>
  <script src="path/to/respond.js" type="text/javascript">
  </script>
<![endif]-->
</head>

Webkit serves as the rendering engine for popular browsers such as Safari and Chrome, among others. Each browser relies on a rendering engine to display HTML/CSS web pages.

Specifically, Internet Explorer once used Trident (now discontinued), Edge utilized EdgeHTML which was a clean-up fork of Trident, Firefox employs Gecko, Opera previously used Presto but has since transitioned to a system similar to Chrome, and Safari continues to rely on WebKit. As for Chrome, it utilizes Blink, which is a variant derived from WebKit.

If you are interested in learning more about WebEngines, particularly webKit, check out this informative documentation found at: WebKit Wikipedia page