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Statistical signal processing is an area of signal processing dealing with signals and their statistical properties (mean, covariance, etc.). It is primarily dealt with in the field of electrical and computer engineering although important applications exist in almost all scientific fields.
The fundamental idea is that a signal is modeled not as a specific function of (for example) time (i.e. y(t)=sin(t)), but rather a function of a random variable (i.e. y(t) = A + N(mean, variance), a constant value with added Gaussian noise). Given information about the random variable, we can increse our knowledge of the output signal, or conversely, given the statistical properties of the output signal, one can infer the properties of the underlying random variable.