Certificates are similar to achievements or titles in other games in terms of bragging rights, but they don't impart any particular advantages or abilities. Essentially, certificates are part of the New Player Experience (NPE), but will provide side benefits for older players as well (particularly in terms of corp recruitment). Certificate rankings progress through Basic, Standard, and Elite, and will be offered in three main groups -- general-purpose, specialist, and new player.
General-purpose certificates will encompass skills like gunnery, tanking, and leadership. Specialist certificates are more involved, covering the ability to use specialized equipment such as jump portal generators and interdiction launchers. But perhaps most significant are the new player certificates. Greyscale writes: "There's a class for each combination or race and starting specialization, giving 24 classes. When you first log into the game, you'll qualify for the Basic certificate of the relevant class. Working up through those certificates will get you into bigger and better frigates, up our skills in certain key areas and eventually get you into a cruiser- or hauler-class ship with the basic skills needed to use it well. This gives new players a very clear (but entirely optional) path to follow for skill training which will eventually get them into a bigger ship with all the right supporting skills."
Greyscale also states that certificates are currently on the test server. The dev blog shows a screengrab of the new Certification Planner, but a number of players are already posting screenshots of it as well. In a related forum thread, EVE developer CCP Chronotis addressed a few player concerns regarding certificates and medals, namely privacy concerns (set to private by default), whether or not medals can be refused (they can),and whether medals given to a player by their corp remain with them after they've moved on to other organizations (they do). For more information on this new feature in the game, see CCP Greyscale's primer "Certificates: Planning the Future."