The advantages of Amazon S3 are reliability, scalability, speed and cost. Here is some info on each.
Reliability: Amazon stores your data in multiple data centers. If there was a disaster and one data center was destroyed your content would continue to be served from the second data center. It’s very unlikely that data you upload to Amazon would ever be lost.
Scalability: If one of your web sites becomes popular and millions of people visit the site, your web server will not be able to handle the load. In comparison when you upload your files to Amazon they are stored in multiple locations. If the load on your content grows your files are automatically replicated to more servers so your files will always be available.
Speed: Amazon has a service called CloudFront that works in conjunction with Amazon S3. When you activate CloudFront on your S3 content your content is moved to edge locations. These are servers that make your content available for high speed transfer.
Cost: With Amazon S3 you only pay for what you use. If you have a few files that get little traffic you will only pay a few cents a month.
SprightlySoft has a blog post which gives even more reasons why Amazon S3 is great. Read it at http://sprightlysoft.com/blog/?p=8