Is inversion of control essentially just retrieving a set of already instantiated objects? In theory. I guess more granular details as implemented by IoC frameworks like Spring have a lot more functionality, but in theory it seems like IoC containers operate like a collection of instantiated beans (in the Java world) and then you get access to those beans. Almost like you would with a collection Singleton objects?
It's partly getting hold of singletons in practice, yes. Some beans will be instantiated multiple times, whenever they're needed (depending on the configuration), but often you can make do with single instances - particularly if they're stateless once configured. I like the idea of data flowing "through" an application's plumbing after it's been properly hooked up.
The benefit is that the "singletoneity" is only present in the configuration, not in the code, which makes the system more testable and flexible. The difference in terms of how you view (and expose) the dependencies with your app is huge.
Although the answer has already been accepted, I will elaborate a little more:
Initially spring was mostly about singleton management. with the introduction of custom scopes came the web specific scopes and the ability to create your own custom scopes. Leaning on AOP features this also allows you to "stay singleton" for as long as possible, because it uses a technique known as scope proxying. This can let you introduce a scoped object right in the middle of a chain of singletons - a feature you'd often be using threadlocals for.
So I'd say it's about tight control of instance creation, to make sure everything is done only the required number of times, and preferably only the construction that is necessary is done for each request. Singleton management was the old days.