These doohickeys "are military-grade implants that significantly increase a new pilot's skill development [...] Capsuleer training renders it ineffective after a while; as such, it will cease to function for pilots who have been registered for more than 35 days," according to the website.
Pilots will also receive a rare frigate (an Apotheosis) if they can manage to invite a friend via EVE's buddy program and convince said friend to upgrade to a paid account.
[Update: CCP has also announced that its Power of 2 special offer is back (through November 28th). Existing players can create an alt account and get 180 days of free game time or three PLEX, for $49.95. Additionally, your character on the new account will receive a cerebral accelerator.]