"Cloud bursting is a technique used by hybrid clouds to provide additional resources to private clouds on an as-needed basis. If the private cloud has the processing power to handle its workloads, the hybrid cloud is not used. Take for example a web application running privately in a data center that is taking online orders. When it reaches peak capacity due to high web traffic, an option is to burst and provision servers on a public cloud to handle additional loads so that all orders can be processed on time. Due to the elastic and on demand nature of public cloud computing, this is possible because you can essentially only pay for the time you provisioned servers during the burst event."
in other words
Getting more cloud power when you need it.