An exact science is any field of science capable of accurate quantitative expression or precise predictions and rigorous methods of testing hypotheses, especially reproducible experiments involving quantifiable predictions and measurements. Physics and chemistry can be considered as exact sciences in this sense. Systems Biology, especially theoretical and mathematical systems biology can also be considered an exact science, as it makes heavy use of mathematical graph theory, logic, statistics and ordinary differential equations.
Of course the word "exact" is not to be taken literally. All science includes some limited observational error, measurement uncertainty, and variation among replicated experiments. Statistical methods are a vital part of all sciences.
The term implies a dichotomy between these fields and others, such as the humanities.