There are three main types of mobile applications: native, mobile web, and hybrid. Hybrid applications combine features of the other two types by allowing installation on devices and working offline like native apps, while using web technologies for cross-platform development like mobile web apps. Flex 4.5 is a technology that can be used to rapidly develop cross-platform hybrid mobile apps for iOS and Android. It provides controls, layouts, and APIs to build apps that look and feel native, but are coded once and deployed across platforms. Developing with Flex 4.5 involves setting up the iOS developer program, dealing with differences in devices, and bundling the app for emulators and devices.