Basically AWS provided a number of IT as service options.
They provide IAAS (infrastructure as a service)
Which is the means of a company having all the servers and network abilities without the need to invest in the equipment. This is hosted off site by Amazon in in a data center and the user within the company simply connect via the internet and they are none the wiser. The benefits again are no upfront costs for the company as well as maintence, storage etc cost also no need to pay an employee to look after this as Amazon can provide this. It can also be scaled to the needs of the company for example if they expect there website hits to go up maybe due to a marketing campaign AWS can increase the abilities of the Web server for this time and then decrease when required. I think this probably what you would be after PM if you want more details as this is what I do I am a cloud engineer and cloud even look into setting this up for you?
As Darren said, AWS provides an infrastructure. You pay for servers and services as used, and the more you use, the less you pay per unit time.
The main advantages to using a cloud service like AWS over your own gear are these (mentioned briefly by Darren):
There is no up-front capital equipment cost.
There is no need for ongoing power, cooling, and hardware replacement costs.
You still probably need your own sysadmins since these are "your" systems, even if virtual ones, but Amazon deals with a lot of the stuff your sysadmins usually would have to deal with, such as checking system health, etc. Your sysadmins still have to deal with system configuration, user accounts/permissions, etc.
If you don't need a server any longer, you can shut it down and no longer incurr costs associated with it.
You can spin up a bunch of servers on short notice if you suddenly need more processing power.
They have good (and inexpensive/reliable) data backup capabilities.