There's an outline of the different versions and what they mean on the main documentation page:
The V2 software may be used to build with our standard tracking on OSX or Linux, or with tool tracking or touchscreen-style gestures. However, many of the development assets associated with V2 are outdated, and the software is no longer supported. We strongly recommend using the more recent software versions.
The V4 software, or the second generation of Orion, is further optimized for performance on VR platforms. With V4 we deprecated the older APIs in favor of the LeapC API, which is significantly closer to the metal. The newest demos such as Cat Explorer require V4. As part of the V4 release we also shared our wrapper for the legacy language bindings, which makes it easy to integrate legacy-reliant applications with LeapC. You can find the binding tool here: github.com/leapmotion/LeapCxx.