What is Cloud Bursting?
Cloud bursting relates to hybrid clouds. The idea is that a given application normally runs in a private cloud or a local computing environment. If a situation arises where the application needs additional resource (computing power, storage, etc.), it can "burst" into the public cloud and use Cloud Computing for those additional resources.
Of course, this can add complexity to the application design. There are vendors that provide hybrid cloud solutions that facilitates taking advantage of cloud bursting.
More on the general topic: Cloud Computing FAQ