An Elastic IP address (EIP) is a static IP address designed for dynamic cloud computing.
According to Amazon, "with an EIP, you can mask the failure of an instance by rapidly remapping the address to another instance. Your EIP is associated with your AWS account, not a particular instance, and it remains associated with your account until you choose to explicitly release it."
For more information see http://docs.aws.amazon.com/AWSEC2/latest/UserGuide/elastic-ip-addresses-eip.html