The MonoBehaviour class is the base class from which every Unity script derives, by default. When you create a C# script from Unity’s project window, it automatically inherits from MonoBehaviour, and provides you with a template script. See Creating and Using scripts for more information on this.
For an complete reference of every member of the MonoBehaviour class, and its technical details, see the MonoBehaviour script reference.
The MonoBehaviour class allows you to start, stop, and manage Coroutines, which are a way to write asynchronous code which can include waiting for a certain amount of time, or for certain actions to complete, while allowing other code to continue executing.
The MonoBehaviour class provides access to a large collection of event messages, which allows you to execute your code based on what is currently happening in your project. Here are a few of the more common examples. For a list of them all, see the Messages section on the MonoBehaviour script reference page
Start - called when the GameObject begins to exist (either when the Scene is loaded, or the GameObject is instantiated).
Update - called every frame.
FixedUpdate - called every physics timestep.
OnDestroy - called when the GameObject is destroyed.