A custom recovery is used for installing custom software on your device. This custom software can include smaller modifications like rooting your device or even replacing the firmware of the device with a completely custom "ROM" like OmniROM

You can find the source code for TWRP at github.com/omnirom/android_bootable_recovery/

CyanogenMod is a customized, aftermarket firmware distribution for several Android devices (See above for supported devices & how to install CyanogenMod on said devices). Based on the Android Open Source Project, CyanogenMod is designed to increase performance and reliability over Android-based ROMs released by vendors and carriers such as Google, T-Mobile, HTC, etc. CyanogenMod also offers a variety of features & enhancements that are not currently found in these versions of Android.