Amazon Silk is the name of the cloud-accelerated browser designed specifically for Amazon’s mobile portfolio. 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 Fire.
While we weren't too kind to Silk in our Kindle Fire review, a lot has changed since that debut. On the Fire Phone, Silk was just as smooth as Chrome is on Android -- at least as far as the layperson could tell.
It's worth noting that in the only browser tests where we could compare apples to apples (SunSpider and Rightware Browsermark), the Fire Phone performed nearly 3x better than the Kindle Fire. Of course, the competition has steadily improved as well, but we thoroughly enjoyed the browsing experience with Silk. We missed Chrome and our synced tabs, but we couldn't complain with overall performance. In fact, in Browsermark, which incorporates a few HTML5 graphics tests as well, the Fire Phone was able to edge out both the Galaxy S5 and the HTC One M8.