I made a brief graphical overview of Core Audio and its (containing) frameworks:
The framework closest to the hardware is Audio Unit. Based on that there is OpenAL and AudioToolbox with AudioQueue. On top, you can find the Media Player and AVFoundation (Audio & Video) frameworks.
Now it depends on what you want to do: just a small recording, use AVFoundation, which is the easiest one to use. (Media Player has no options for recording, it is – as the name says – just a media player.)
Do you want to do serious real-time signal processing? Use Audio Unit. But believe me, this is the hardest way. 🙂
With iOS 8.0 Apple introduced AVAudioEngine, an Objective-C/Swift based audio graph system in AV Foundation. This encapsulates some dirty C-stuff from Audio Units. Due to the complexity of Audio Unit it is maybe worth a look.
Further readings in the Apple Documentation:
- Core Audio Overview: Introduction
- Multimedia Programming Guide
- Audio & Video Starting Point