What is S3?
S3 stands for Simple Storage Service, an online storage service that allows you to store unlimited files in the cloud.
Why would I use S3 instead of a regular host?
Regular shared hosting providers charge you a fixed amount every month. That's regardless of the amount of files you store or the amount of visitors you get. Most cheaper webhosting companies also don't cope well with high traffic websites. Suddenly got featured on Reddit or Hacker News? A regular hosting provider might suspend your account for all the traffic! With S3 you only pay for what you use and it's highly scalable.
What does it cost?
To give you an example of cost: when my blog receiver 1000 visitors per month I was paying just 6 cents to host it!