Wikipedia defines Cloud computing as “the delivery of computing as a service rather than a product, whereby shared resources, software and information are provided to computers and other devices as a utility (like the electricity grid) over a network (typically the Internet)".
Put in simpler terms, Cloud computing is a way to describe how organizations can offset some or all of the existing IT infrastructure and operations to IT professionals, allowing them to configure and manage systems. This allows the business’s internal core team can focus on new ways to help the business at hand, rather than becoming experts in building servers, managing storage, or protecting data.
Elasticity is one component of Cloud computing. By using automation and workflows, the data center can scale up or down as required by the applications that are consuming resources. A practical example would be a popular online retailer on Cyber Monday which needs to expand resources to respond to increased demand during the holidays. They need responsive servers to meet those increased demands and then shrink back down after the holidays again, dynamically scaling up or down.