Akamai run a content distributions system used by major websites to provide fast web response on a global scale.
Port 443 is used for HTTPS - the encrypted version of HTTP web-page access.
It is quite normal to see a lot of traffic directed through Akamai.
At the time this question was asked, Apple used Akamai as their primary content delivery network.
On July 21, 1999, at Macworld Expo New York, Apple and Akamai
announced a strategic partnership to build Apple's new media network,
QuickTime TV (QTV), based on QuickTime Streaming Server. Both
companies later announced that Apple had made a $12.5 million
investment in the company the previous month. Apple continues to
use Akamai as their primary content delivery network for a wide
range of applications including software downloads from Apple's
Website, QuickTime movie trailers, and the iTunes Store.
Apple (NASDAQ:AAPL) recently launched its iCloud service that allows
users to store their music, photos and other documents on the cloud.
This content is thus accessible from Apple’s mobile devices and any
PC. While this is certainly a shiny introduction from Apple to fuel
the growth in sales of its iPhone and iPad devices, it also holds
promise for Akamai (NASDAQ:AKAM). As a content delivery vendor for
Apple, Akamai has an advantage over its competitors
Akamai's servers and Apple's datacenters are being hammered for OS X Lion downloads.