IASS stands for Infrastructure As A Service. Wasn't that easy to understand? Infrastructure here means all the servers, the switches, the storage, the ups, the firewalls, the routers and any network equipment that normally sits in your "server room".
Imagine you are working for an SME. A company falls under the SME category if it has less than 500 employees. You usually have a small room where you put all your servers and not surprisingly you call it a "server room". You will have all your network equipmenta there, with Internet connectivity, UPS and so on. To manage these servers you will probably need IT personnel, 24/7 support and availability, UPS, monitoring, rack space, electricity and so on.
And usually not all the resources in your server room are fully utilized. Most of the times the servers are idle and under utilized and at peak hours you experience spikes where your servers cannot take the load. Therefore you have lots and lots of limitations when you have your own data center or server rooms.
IAAS on the other hand solves these issues and brings more benefits. The whole data center is now available as a service in a pay per use basis and you no longer have the headache of managing your own server rooms. When you have spikes you can automatically increase your processing power and reduce when you don't need and pay only for what you use.
Big players like amazon have invested heavily on this and currently the leader in IAAS. They call it Amazon Web Services. With this you can get a server with just a few clicks and the server get running in few minutes. You can choose the power you need, the storage space you require, the bandwidth you require and it is usually payable by the usage.
With the IAAS providers doing all the hard work you can rest assured that your servers are always available with the state of the art data center and fully secure.