What are CyanogenMod and MIUI based phones? Recently I came to know about some phones which are based on MIUI and CyanogenMod. I want to know if the meaning behind it is they will get lifetime updates from MIUI and CyanogenMod or something else?
CyanogenMod OS is a custom ROM derived from Google's Android OS.  It is available for large number of devices and delivers updates as nightlies, release candidates, betas, snapshots etc. Frequency of updates depends on the type of ROM flashed onto the device.
MIUI (Mi User Interface) is also a custom ROM which is based on both Google's Android and CyanogenMod but has a home-cooked and customized interface developed by a Chinese firm Xiaomi Tech. It highly resembles Apple's iOS interface. MIUI is available for some flagship phones from popular brands.  


All the devices running on CyanogenMod and MIUI gets updates very frequently than others. Updates occur over-the-air (FOTA). As a bottom line they are used as stock firmware replacements.