The formal definition of Fischer Information is:
"For random variable X, with a likelihood function $ L(θ,X) $ and score function(with respect to parameter θ) $ s(θ;X) = \nabla [ln(L(θ,X))] $(Rothman)
In more understandable terms this just means that for some probability density function, the amount of information stored in the parameter θ, or Fischer information $ I(θ) $ is equal to the variance of the score.
