What is an IoC container?
What is an IoC/DI framework?
Why do we need a framework for IoC/DI?
Is there any relationship between IoC/DI and AOP?
Martin Fowler has a good article here on the meaning of Inversion of Control and Dependency Injection.
Spring.NET usage AOP is described in detail here. I'm more familiar with the Java-based version of Spring, so I cannot say with absolutely certainty that Spring.NET currently only supports proxy-based AOP.
That is, a class to be advised must implement an interface. Spring will create a dynamic proxy that implements this interface and delegates to the original target instance.
Although it does state:
In a future release we will implement proxies using inheritance, which will allow you to proxy classes without interfaces as well and will remove some of the remaining raw reference issues that cannot be solved using composition-based proxies.