Traditioanlly, apps that you use on your phone are built to run specifically, and only on the type of phone you have. if you use facebook on your iPhone, you are using an app made by the Facebook Development team speifically for iPhone - they will not work on an Android. These apps are refered to as Native Apps.
Hybrids are apps built to run on mutiple platforms, built once, they can run on iPhones, Androids, Blackberrys, TV sets, computers etc.
Your choice of whether to go Hybrid or Native is going to be made based on the requirements of your app; the functions the app needs to do, the way you wish to work with and maintain that app, where your app is going to be used, who is going to use it, the timing for delivery and your budget.
At Toledoh, we focus on building Hybrid Apps they are generally faster to build and less costly to deliver. We find that in most cases we are aiming for greater market penetration and as such the ability for a one-size-fits-all approach is generally the best option.
Hybrid Apps can be seen as a mix between "native" apps and web sites. Basically, we build a website then wrap some code around it so it becomes an app. This "wrap" takes advantage of all the cool phone features like cameras, geo-location etc, and are configured for multiple devices at once.
Because the app at its core is very similar to a website, we can then take advantage of our web systems, processes and experience. We build with Nuts'n'Bolts to allow the content of the app to be maintained, so you don't have to keep on paying developers each time you need to make a change, update a page etc. We don't have to reinvent the wheel.
If you already have a website that you maintain with Nuts'n'Bolts, you can push that content and functionality in mobile apps quite easily. A single login to the admin to maintain your website, also allows you to maintain your apps. Any processes and functions utilised by your website (think members access, shopping carts, notifications, 3rd party integrations) can all be accessed via the apps.