Put simply: The "Application Context" is another name for the Spring container. Spring's primary job is to manage the lifecycle and relationships between a lot of objects. It does that by loading them in its container.
To load the container..well there are several answers to that, depending on how you build your application. Typically, there's one or more XML files that contains one or more <bean> declarations (although these XML files keep getting smaller thanks to some special namespaces, annotations and autowiring).
If it's a web application then those XML files are loaded by either DispatcherServlet and/or ContextLoaderListener. If it's an OSGi bundle, then they're loaded by the Spring-DM extender. If it's a standalone (e.g., has a main() method) application, then you might load them a little something like this:
And there are other ways to load it...kinda depends on the circumstance, though.