Silk Browser & Performance
Amazon Silk is the name of the cloud-accelerated browser designed specifically for the Kindle Fire. It uses what Amazon calls a "split browser" architecture, which is a fancy way of saying some web computation chores are offloaded to the Amazon Elastic Compute Cloud (Amazon EC2). This works in tandem with the local browser and hardware, the theory being that it should load pages quicker and won't bog down the Kindle Fire.
In practice, Amazon oversold the experience. You can read about Amazon's Silk browser architecture in much more detail here, just don't wet your pants in excitement thinking this is a totally new browsing experience. It's not, and worse yet, webpages consistently stutter when you scroll. I wouldn't call it a broken browser and it's definitely usable for farting around the web, but after engaging Amazon's hype machine, you'll expect a lot more. Perhaps the experience will improve over time with updates but this remains to be seen.
Glorified eBook reader or a bona fide tablet? You're not going to answer that question with Linpack. Overall, the Kindle Fire posted a fairly strong score that's about on par with some older tablets and high end smartphones.
The Kindle Fire's SunSpider score, while respectable, is a bit heavy and is more in tune with a high-end smartphone than a top-tier tablet. This is probably due to Amazon's heavy modification of not only Android, but the Silk browser itself.