What does cloud computing offer your organisation? The definition of cloud is that it has to be broadly available, self-service, measured, elastic and able to work against resource pools. The first three of these are pretty self-explanatory - the Internet allows cloud systems to be available on a worldwide basis, and users are getting used to selecting their own services and receiving reports on the performance of systems and what they have used.
The last two are where it gets more interesting, though. Resource pooling brings together all of the available processor, storage and network systems and makes them available for sharing. Elasticity takes these pools and allocates them to different workloads on a dynamic basis - the workloads get the resources they need, as they need them.
Sounds great - the trouble is, it's not so easy with private cloud. Let's assume that you have, say, 100 different workloads across 200 servers. It's likely that your current processor utilisation rates are around the 20% level. Using private cloud and sharing the processor resource across all the workloads may allow you to get rid of some servers and drive utilisation rates on the others up to around 80% - but you'll still hit the ceiling of available resources unless you heavily over-engineer.
Now let's consider a public cloud provider. It will have hundreds or thousands of customers with tens or hundreds of thousands of different workloads. This provider has resource pools that are massive - even when running at 90%+ utilisation, it will have more spare resources than you would have in your entire private data centre.
This allows for great flexibility - new products or services can be brought to market more easily; new ideas can be tried out - and thrown away if they don't work.
Flexibility of resources was key to Turkish open source systems integrator, Profelis. It chose Microsoft Azure as a means of providing variable but scalable I/O around Profelis' Linux instances, using Azure's flexibility to easily add resources as new products and services were brought to existing and new markets.
Profelis understood how to flex the muscles of the cloud - maybe you should do the same?