AWS = Amazon Web Services = a suite of different web services.
S3 (which you linked to) is an object store. You can't host a web service on S3.
EC2, also under the AWS umbrella, is virtualized compute space. You CAN host a web service on EC2. It is just like having a server in a rack somewhere, except that when you shut down an instance, it is gone forever. But using EBS, which is like a virtualized hard drive, will prevent you from losing your data when the EC2 instance shuts down.
See http://aws.amazon.com/ec2/ and http://aws.amazon.com/ebs/