It's curious that a straightforward question has been voted down. The previous poster made some vague claims about IE being "plumbing" and the best alternative for some "things it can do" but doesn't mention what they are. Other than ActiveX integration which is not exactly a stunning recomendation.
I guess one main difference is that a plugin for Internet Explorer can do so much more than a plugin for Chrome can, and that the basic philosophy for IE is that it's a relatively thin wrapper around mshtml.dll, one of the most deservedly overutilised pieces of software of the past decade. Sure, you can embed Webkit in things, but it hasn't happened all that much quite yet. Webkit has even been designed for that, in some part.
But Internet Explorer has perfected it back in about '97, and that's the legacy that IE is still built on. It has been doing VML since '98, and that serves as the foundation of a canvas implementation that works even in IE6. XMLHTTP has been in the thing in '99. You could run ActiveX widgets in IE. That was the biggest feature of them all, probably, and it's still widely used. Maybe not here, but in China, IE's market share in May was 72%, not including IE shells. Not least of all because all the banks usually want some ActiveX plugin that keeps your keyboard entry more secure (whatever). Chrome and Firefox were 15%. Combined. South Korea, in July 2011? More than 92%.
Horrible a browser as IE6 was and still is, the target market was rich application software that could use things like DirectX and VML and VRML and XMLHTTP and all these kinds of outdated technologies that we've left behind once Mozilla arrived and gave us some fresh air.
Sure, IE didn't do much in the way of progress in terms of the Acid Test or JavaScript or CSS or HTML, but that was because the target market wasn't really the same. The target market for IE was business in the early 2000s. And it succeeded spectacularly, leaving a bad browser to drive oft-rotten legacy applications.
It has provided a stable set of features for almost 15 years. They may not be the best technologies... but the implementation was good enough. And all of that in a browser that had a 95% market share. There are so many hooks and places where IE can be extended that are a bit mindblowing. IE6 was a sucky browser around a fairly well thought out ecosystem that was settled. There are still things that can be done in IE that can't be done in Chrome. It was sucky, but it worked, and IE has a thousand features in the background that most people never even noticed. That, and group policies.
That said, I hate IE6 and IE7 as well as those F12 Developer Tools with a passion that will burn a thousand years. But it's not all bad.
I agree the browser is not all bad if you take into account the original target market. But I stand by my surprise that even after the writing has been on the wall for so long, times clearly changing even in the enterprise market, MS still hasn't made it a priority to improve the day-to-day experience for today's user.
What things are those?