You get the entire gamut of features related to the API that do not rely on Apex Code (because you still don't get Apex Code). This includes the Bulk API, REST API, SOAP API, Streaming API, Metadata API, and Tooling API. What you don't get are custom REST and SOAP APIs (because there is no Apex Code). It is possible to have the external system connect to salesforce.com via any of the available APIs specified in the list, and it is possible to access external systems (JavaScript only) using custom buttons, links, and Visualforce pages.
Purchasing Webservices API is primarily for the intent of having external systems communicate with salesforce.com, not the other way around. This means that, assuming AS400 has the ability to run automated tasks, it can periodically query the salesforce.com servers for new data, update records in salesforce.com, and so on, but salesforce.com will not actively initialize a connection to the AS400 without user interaction.