I made a brief graphical overview of Core Audio and the 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 most 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 hardest way. :-)
With iOS 8.0 Apple introduced AVAudioEngine, an Objective-C/Swift based audio graph system in AV Foundation. This encapsulate 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:
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…