The principle is simple, the unlicensed bands such as the 2.4 GHz and the 5 GHz ISM bands are overused thanks to WiFi and Bluetooth and some of the licensed band are on the contrary underused.
So the idea is to use the unused spectrum resource without interfering with the “legitimate” service.
Easy to say but difficult to perform since this means that the Cognitive system needs to be aware of the ever changing environment and adapt itself in real time to maximise the use of the spectrum without interfering with other systems.
We could actually push further the concept and not only limit the system to a coexistence with legitimate systems but use the adaptive intelligence to choose the most efficient available resource for a service. One example could be to use WiFi for data and the cellular network for voice and if the voice network is not available use VoIP and the WiMax network. (Well I’m probably pushing too hard the concept)
I’m not a big fan of Microsoft but they are leading a project that is worth to mention : KNOWS as for Kognitiv Networking Over White Spaces.
They define the KNOWS system as “a system encompassing new hardware, an enhanced MAC protocol and spectrum sensing capabilities, for efficiently utilizing unused portions of the licensed spectrum for unlicensed operations. KNOWS cooperatively detects incumbent operators and efficiently shares the vacant spectrum among unlicensed users.”.
Please refer to the references for further information.
I found another interesting article in the http://arxiv.org/ that gives the following definition :
“This technology is capable of dynamically sensing and locating unused spectrum segments in a target spectrum pool, and communicating via the unused spectrum segments without causing harmful interference to the primary (licensed) users of the spectrum. Primary users are defined as users of existing commercial standards. If a higher priority entity, e.g., a primary user demands the channel, the CR (Cognitive Radio) users should vacate and find an alternative channel.” 
What I found more interesting is that they categorized three kinds of Cognitive Radio behaviours:
1) Interference mitigation: Both the Cognitive Radio and the primary users can simultaneously transmit at the same time or frequency bands.
2) Collaboration: Cognitive Radio users act as relays. I found this a very complicated solution.
3) Interference avoidance: Cognitive Radio users transmit over a certain time or frequency band only when there are no other users. I’m guessing this will be the most implemented solution.
And last but not least they propose a fourth category.
4) Interference mitigation : The develop more on this solution using dirty paper coding.
Dirty paper coding is a promising precoding technique for cancelling arbitrary interference perfectly known only at the transmitter but not at the receiver. (I’m learning this as I write)
But there is a downside, in order to apply Dirty paper coding in the Cognitive Radio the authors of the paper assume that the codewords of the primary users, as well as their channel gains are non-causally known at the CR transmitter (TX). This assumption will only stand as long as the Cognitive Radio and the primary TX are close enough to each other.
The other characteristic of the system is that the Cognitive Radio Transmitter not only transmits its own signals but also relays those of the primary users.
This is when things get intense since they will treat the system as a MiMo System where for Cognitive Radio receivers signals from primary TX and those relayed by CR TX are interferences and vice versa.
And yes you can guess what does the channel model look like :
Where the channel gains between primary TX and RX, primary TX and CR RX, CR TX and primary RX, and CR TX and RX are denoted by H11,H21,H12,and H22 respectively. The power constraints of the primary TX and CR TX signals Xp and Xc are denoted by Pp and Pc respectively. The unidirectional arrow from the primary TX to the CR TX means that the CR TX knows the primary user’s codewords non-causally.
From this model they will continue their work. So do not hesitate to keep on reading the original article.
And just for your curiosity their simulation results showed that the proposed method with reduced-complexity computer search has performance approaching the optimal linear assignment rates. Not so bad.
References and further reading
 Cognitive Radio with Partial Channel State Information at the Transmitter