The geometric mean is a number, which is used to represent a set of numbers. It is calculated by taking the n-th root of the product of these numbers. What most people refer to when they talk about mean or average is the arithmetic mean. The geometric mean is almost always smaller than the arithmetic mean. In some cases, it is equal. The geometric mean is often used in finance and in statistics.
Because there's a product, it does not make sense to calculate the geometric mean if one of the numbers is zero. It generally also does not make much sense to calculate it when one of them is a negative number. It isn't used for complex numbers, because calculating the root of a complex number has more than one result.