Recovery is a dedicated, bootable partition with recovery console installed. A combination of keys (or command line instruction) will boot your phone to recovery, where you can find tools to repair your installation as well as install official OS updates. The stock recovery has very limited functionality, it provides very limited commands which can help you recover your OS. This is where Custom recoveries come into play.
A custom Android recovery replaces stock recovery. It can do all the stuff as a stock recovery and it provides you more options to control your device. Using custom recovery, you can install official and unofficial ROMs, themes, kernels, wipe different partitions of your device, mount the external SDCard or even USB mass storage devices, fix permissions, perform backup & restore and much more.
TWRP, ClockWorkMod (CWM) and Philz Touch Recovery are most widely used custom recoveries which offers plenty of features to users. For more information on custom recoveries, visit this website.