I think it's easier to understand how apigility can help you if you first understand what REST is all about. You can find all sorts of long, academic explanations of REST, but for me it all boils down to using the full power of the HTTP protocol.
If you've done any web programming, you are probably familiar with the verbs GET and POST, but HTTP also specifies several other verbs that you probably haven't used including PUT, PATCH, and DELETE. The standard way of using these verbs is like this:
GET - retrieve one or more existing resources
POST - create a new resource
PUT - replace an existing resource with a new one
PATCH - modify a resource in place (update only certain fields)
DELETE - delete an existing resource
You can see that HTTP provides you everything you need--right out of the box-- to create, read, update, and delete data. By leveraging these standards, you save yourself time in designing your API and make it easier for users of your API who are familiar with REST to get started using it.
What apigility does for you is take away a lot of the drudge work like: setting up routes, creating classes, and generating documentation for you. It also allows you to use ZF2's tools for things like input filtering and validation that you will want as your API grows.
For example, you might want to allow your users to interact with "widgets" in your system. With just a couple of clicks, apigility will generate stubs of all the classes you need for someone to be able to do all the common REST verbs on your "widget", along with basic documentation. It will also give you friendly urls like /widget instead of /script.php?thing=widget or some nonsense like that.