A number selected by chance (or in the case of a computer program, as near to simulating chance as possible).
Typically, a programming language has a built in command or function to generate a number for you. In most cases, the number will be delivered as a random floating point decimal value between 0 and 1. It is up to the programmer to apply arithmetic to this number to convert it to a number in the desired range.
For example, if you want to simulate the roll of a six-sided die, you would multiply this original random result (which starts out between zero and one) by six, add one and then remove any portion after the decimal.
In the most extreme cases, where RandomResult is 0 (multiplying by six yields zero, and then add one) our die roll is a one, and when RandomResult is 0.999999... (multiplying by six yeilds 5.9999..., adding one yeields 6.9999..., but taking only Integer portion) we get six.