The monkey is an application which runs on your device or emulator and creates fake pseudo-random events in the form of touch, clicks, swipes, and other user actions. You can then use this data to test out software that you're developing, in a repeatable yet unpredictable way. For example, if you're developing a game, you may wish to make sure that it's bug-free before releasing it into the market, so you can create a series of fake users to play the game on and see if any of them have any problems with the software.
Monkey comes with an Android device simulator, which you can use to test your software with. With this software, you have a very good idea of how the software behaves when it's not running on the device itself. You'll have access to both an "Emulator"Virtual Device" to test your software on real hardware. If you don't want to bother using this Android simulator, you can instead use a real device to run the software on. In this case, you can also have access to the "Real World" application from within the Android app. Using the Android app is more convenient since you can see how the application behaves when you try to use it on real hardware.
The downside of using Monkey is that it's not available on many devices right now (e.g., it's only available for the LG G Pro). If this is the case, however, you can still test your software on real hardware by using the Real World application instead. This is a third-party Android application which will also let you get some good performance data from your software. It also includes a "Network Analyzer" and other useful tools to help you get some good performance data from your application.