There are as many definitions of cloud as there are technology bloggers. However, the major theme is that a Public Cloud provides IT resources that are provisioned remotely from the consumer and operated by a third party.
In a Private Cloud, the infrastructure policies are governed by a single organization where workloads and data can be moved to and from internal and external data centers. Private Clouds provide an organization a single point of control for security, manageability, privacy, audit, compliance and governance.
However the business case for engaging in a public or private cloud strategy involves several factors, the most important being business revenue and/or budget.
Picture is Worth a Thousand Words

[...] the same vein:Infographic: Public vs Private Cloud Is GDrive Finally Being Launched?After 2010 Feats, EMC Awaits Challenges From New ContendersEMC [...]
[...] to simplify the often overwhelming course of achieving a specific goal is a classic example of how cloud tools are now leaning towards individualized services. The website efficiently directs you to potent [...]
[...] is this rather definitive cost breakdown as reported by John Furrier through this SiliconAngle.com blog that argues in favor of private clouds as the better investment, in terms of pure ROI. As you can [...]