Karma is unique to every board. For example, if you give karma on the Elemental boards, that karma will only be visible on the Elemental forums. The same goes for GalCiv, SoaSE and so on.
Not precisely true.
Karma given on one site will in fact appear on another site as long as the thread that is the source of that karma exists in a forum that is visible on both sites *and* only if the person has actually received karma from both sites.
Take the Off-topic forum for example. The Off-topic forum (/forum/412) exists on many different sites. Say that someone's primary site is the GalCiv2 site, then on the GalCiv2 site they will have a significant amount of karma and perhaps on the Elemental site have no karma. Then suddenly someone on the Elemental site decides to give that person karma for a post in a thread in the Off-topic forum. Suddenly that person will not only show the karma newly received from the Elemental site on the Elemental site but will also get "credit" on the Elemental site for all the karma received from *any* forum and *any* site that shares that forum with the Elemental site.
Basically you will get credit for karma received from any forum on any site that has that forum but only after it has been "enabled" by your having received at least 1 point of karma from that particular site.