Amazon S3 provides scalable and fast data storage in the cloud. It allows users to write, read, and delete objects ranging in size from 1 byte to 5 terabytes and store them in different regions. Amazon EC2 offers virtual computing capacity in the cloud. Together, Amazon S3 and EC2 make up core components of Amazon Web Services (AWS), one of the largest cloud computing platforms used for tasks like data analysis, backups, and traffic spikes.