Amazon's Simple Storage Service (S3), found at http://aws.amazon.com/s3/, is a storage service that provides a simple key-value storage model. Using web, command-line, or programmatic interfaces to create objects, which can be anything from text files to images to MP3s, you can store and retrieve your data based on a hierarchical model. In this model, you create buckets that contain objects. Each bucket has a unique identifier, and within each bucket, every object is uniquely named. This simple strategy enables an extremely powerful service for which Amazon takes complete responsibility (for service scaling, in addition to reliability and availability of data).
Amazon's Elastic MapReduce, found at http://aws.amazon.com/elasticmapreduce/, is basically Hadoop in the cloud. Using any of the multiple interfaces (web console, CLI, or API), a Hadoop workflow is defined with attributes such as the number of Hadoop hosts required and the location of the source data. The Hadoop code implementing the MapReduce jobs is provided, and the virtual Go button is pressed.
In its most impressive mode, EMR can pull source data from S3, process it on a Hadoop cluster it creates on Amazon's virtual host on-demand service EC2, push the results back into S3, and terminate the Hadoop cluster and the EC2 virtual machines hosting it. Naturally, each of these services has a cost (usually on per GB stored and server-time usage basis), but the ability to access such powerful data-processing capabilities with no need for dedicated hardware is a powerful one.