Monkey Testing

Testing by means of a random selection from a large range of inputs and by randomly pushing buttons, ignorant on how the product is being used.

Or

Testing a system or an Application on the fly, i.e. just few tests here and there to ensure the system or an application does not crash out.

Or

In computer science, a monkey test is a unit test that runs with no specific test in mind. The monkey in this case is the producer of any input. For example, a monkey test can enter random strings into text boxes to ensure handling of all possible user input or provide garbage files to check for loading routines that have blind faith in their data.

Or

Testers use the term monkey when referring to a fully automated testing tool. This tool doesn’t know how to use any application, so it performs mouse clicks on the screen or keystrokes on the keyboard randomly. The test monkey is technically known to conduct stochastic testing, which is in the category of black-box testing.

There are two types :
1) Smart Monkeys
2) Dumb Monkeys

1) Smart Monkeys : Are valuable for load and stress testing.
                             They will find a significant number of bugs.
                             Very expensive to develop.

2) Dumb Monkeys : Inexpensive to develop.
                             Able to do basic testing.
                             Can find only few bugs.