In short and disingenuously, IaaS can be summed up as "cloud servers."
IaaS is the term used by cloud providers for denoting the idea that you can shift all those dusty, noisy, and expensive on-premises boxes into "the cloud."
In reality, the cloud is just the marketing term for "a bunch of servers in various data centres," and it annoys many engineers who dislike wool-filled terms that only serve to obfuscate and confuse.
The benefits of doing something like shifting your infrastructure into the cloud should be obvious, and we've discussed the idea of Infrastructure as Code (IaC)before.
Gone are the days when deploying a development environment means buying new servers from your distributor, racking and cabling them all, and making sure you've got a decent method of getting your OS of choice on there...