Cloud computing can be simply defined as a service or software which draws resources over online servers (hence the cloud) vs a physical server or device. You essentially store things online to access them online, but at a faster rate and bigger files. Think of Netflix, but with more options than movies and t.v. Shows.
What does that mean to the average Joe of a user you might ask? Well you cab store movies and misc to play at any given moment, make mobile backups of your phone to restore later. Trust me, I've spent 2 hours in an Apple store waiting for my files to transfer from my old iphone to my new one. True pain.
Another more practical use of the service will work and work related activities. Even though you can do work from home or online cooperative work, cloud computing will make it easier and more effective.
So far the only limits of cloud computing is the devices you have to access your data with, tablets and cellphones are the idea targets, then netbooks and laptops, but we well be adding cameras, camcorders and projectors in a few years.(3 or less) Wifi memory cards and cameras with Wifi coming, the ability to store pictures outweighs spending almost $100 on memory cards.
The first three public services are Google, Amazon and Apple. Well Apple comes out later on this year, Google is in beta stages and Amazon is out but limits it's service to music, I will review Amazon later on this week via its android app.