Very often people say cloud when they actually mean public cloud. For this reason, in the book, we'll always specify private cloud or public cloud and when we do not specify anything, the word cloud is used in both senses at the same time.
This is a necessary disclaimer because when speaking of security, private and public clouds have completely different issues, but let's start from the beginning.
A private cloud environment is operated solely for a single organization (or person) by internal or third-party personnel. In a private cloud situation, all machines are owned (or leased) by the organization and will run that organization's software exclusively.
From an economical perspective, private clouds are less flexible; in fact, the number of machines will stay pretty stable over time compared to public clouds.
From a scalability perspective, private clouds are not very flexible because you can't use more processing power than that...