Just like it's named, recovery mode take an act to recover your Android device. In simple way for me, recovery mode is like some "first aid" when something happen to your device. Recovery mode is one of feature in Android smartphones that serves to fix, add, replace, remove (delete), the contents of our Android device or even to upgrade the Android version. Maybe we often hear recovery mode is needed when are to install custom ROM, systemUI mod, or adding tweaks (script to boost performance) to our device.
To put our Android device into recovery mode, turn off the device, and then press the following button: Volume Up + Home + Power, simultaneously and hold its for 5 second. When you are in recovery mode, use the Volume Up and Volume Down button as navigation and Power button as confirmation (in CWM recovery the confirmation button is changed to Home button).
Stock recovery in android
Stock recovery is the default recovery of Android smartphones from the device manufacturer. Features in stock recovery is soooo... limited. And sometimes (many times) if we do an "install from zip" will become failed because "file header verification failed", that is because the device manufacturer is some kind like "protect" the system from being modified. Even on some Android smartphone brand does not have default recovery mode installed. So for the reason, installing a custom recovery is something we can not avoid IF we want to change the system of our Android device effectively
Custom recovery CWM and TWRP
As it says "Custom", not original, it is a recovery mode that is made by 3rd party. In Custom recovery is added some features that does not exist in stock recovery like backup, touchscreen support, file manager, etc. There is two most popular custom recovery used by Android device user, that is CMW (ClockWorkMod) and TWRP (Team Win Recovery Project), although there's another custom recovery like Philz Recovery. Most important thing in custom recovery is ability to disable the "signature file verification", so we can install or flash any file we want without worry the zip files being blocked to be flashed because the signature things just like in the default recovery.
To install a custom recovery we need to find the correct recovery file to our Android device model. We must extremely carefull because different way to install the recovery, different smartphone device model, and the recovery file will be different. If we choose the wrong recovery file or wrong method will cause our Android device unable to enter to recovery mode anymore, or even worse: bootloop or softbtrick.