What is WebKit and how is it related to CSS?

Update: So apparently, WebKit is a HTML/CSS web browser rendering engine for Safari/Chrome. Are there such engines for IE/Opera/Firefox and what are the differences, pros and cons of using one over the other? Can I use WebKit features in Firefox for example?

Every browser is backed by a rendering engine to draw the HTML/CSS web page.

• IE → Trident (discontinued)
• Edge → EdgeHTML (clean-up fork of Trident) (Edge switched to Blink in 2019)
• Firefox → Gecko
• Opera → Presto (no longer uses Presto since Feb 2013, consider Opera = Chrome, therefore Blink nowadays)
• Safari → WebKit
• Chrome → Blink (a fork of Webkit).

See Comparison of web browser engines for a list of comparisons in different areas.

The ultimate question... is WebKit supported by IE?

Not natively.

Addition to what @KennyTM said:

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

¹⁾ On February 12 2013 Opera (version 15+) announces they moving away from their own engine Presto to WebKit named Blink.

²⁾ On April 3 2013 Google (Chrome version 28+) announces they are going to use the WebKit-based Blink engine.

³⁾ On December 6 2018 Microsoft (Microsoft Edge 79+ stable) announces they are going to use the WebKit-based Blink engine.

Webkit is a web browser rendering engine used by Safari and Chrome (among others, but these are the popular ones).

The -webkit prefix on CSS selectors are properties that only this engine is intended to process, very similar to -moz properties. Many of us are hoping this goes away, for example -webkit-border-radius will be replaced by the standard border-radius and you won't need multiple rules for the same thing for multiple browsers. This is really the result of "pre-specification" features that are intended to not interfere with the standard version when it comes about.

For your update:...no it's not related to IE really, IE at least before 9 uses a different rendering engine called Trident.

This has been answered and accepted, but if someone is still wondering why are things a bit messed up today, you'll have to read this:

http://webaim.org/blog/user-agent-string-history/

It gives a good idea of how gecko, webkit and other major rendering engines evolved and what led to the current state of messed up user-agent strings.

Quoting the last paragraph for TL;DR purposes:

And then Google built Chrome, and Chrome used Webkit, and it was like Safari, and wanted pages built for Safari, and so pretended to be Safari. And thus Chrome used WebKit, and pretended to be Safari, and WebKit pretended to be KHTML, and KHTML pretended to be Gecko, and all browsers pretended to be Mozilla, and Chrome called itself Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US) AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.27 Safari/525.13, and the user agent string was a complete mess, and near useless, and everyone pretended to be everyone else, and confusion abounded.