Native applications are applications which run directly on the iPhone hardware. These applications can take advantage of the wide range of hardware innovations that come with the iPhone. These include support for multi-touch, hand gestures, iPhone camera, accelerometer and the built in GPS.
However native applications are much harder to build as compared the web applications. And if you are not too much into programming the obtruse syntax of Objective-C will present to you a very steep learning curve. On the plus side, those who have scaled this curve can use their programming chops to cook up some of the most innnovative applications that are getting enabled by the iphone. Add to that the instant recognition and money that a lot of developers have earned by listing on the iPhone App store, and that should be motivation enough for you to start hacking right now.
Native applications unfortunately require you to invest in Apple hardware if you don't already have some. At the minimum you would need a Mac because the iPhone SDK currently only runs on one. Secondly, you would need an actual iPhone. Even though the SDK comes built in with an iPhone simulator this is not enough because a lot of features don't run the same as on an actual iPhone. Case in point is the accelerometer and multi-touch support both of which are not supported on the emulator.
There essentially two big pieces of technology you need to master to build iPhone native applications: Cocoa and Objective-C.
Cocoa is the platform and the API that iPhone exposes for you to access the low level iPhone functionlity. Apart from this Cocoa also provides the infrastructure to build simple form based applications for the iPhone. As Apple provides exhaustive documentation on the Cocoa API it is pretty straightforward to get started on.
Objective-C is the variant of the popular C language which is used for the iPhone development. Objective-C is pretty much the same as C/C++ apart from the way it structure functions and message passing. Message Passing, or the way Objective-C structures functions calls are a much more object oriented way of programming, however the syntax takes some time to getting used to. For a good overview on the way Objective-C structures message passing visit the wiki page at here
Apart from Cocoa and Objective-C incase your native application is graphics heavy (for example games) it might need to use Open GL to build the graphics part. Open GL is an open source graphics library and is supported on the iPhone. You can read more about OpenGL and iPhone programming here.