Discovery News is reporting that in the microscopic scale, Graphene, a complex form of carbon, conducts heat really well. Graphene would be layered with the silicon and would distribute the heat made by the circuits to the edges of the device. The larger surface area would help it cool off.
This is important because the faster processors of today are getting harder and harder to cool off. The faster they switch, the more power they need, and the more heat they make that has to be hauled away before it melts something. 1980s era personal computers needed a small heat sink. 1990s era computers needed a large heat sink and a small fan. Today's computers need a large heat sink and fan, and thermal paste to facilitate heat transfer to the heat sink.
With this discovery, the entire backplane (like the motherboard in personal computers) can now effectively be used as a heat sink, making the entire cooling process more efficient. The heat radiates into the air, requiring slightly less fan action. This will make computers quieter. Or faster. Probably faster. (Same cooling setup will now tolerate more heat output, so the CPU is clocked even faster than before.)
Good news if you like overclocking. Bad news if you're air conditioning a data center.