Observed frequencies are those which are obtained by observation of the actual occurrences of the frequencies of a variable in course of the experiments. Expected frequencies, on the other hand, are those which are obtained by application of some mathematical model like Binomial expression, Poisson expansion, or Normal distribution model. A comparison between the observed and the expected frequencies can be done either graphically, or algebraically. In the graphic method, both the observed and the expected frequencies are plotted on a graph paper, and if the two curves are similar, or very close to each other, the difference is said to be insignificant and the fit is said to be god. But, if the two curves are pulled away from each other, the fit is said to be poor, and the difference between the two frequencies is said to be significant.
In the algebraic model, the absolute differences between the observed, and the expected frequencies are found out, and then various tests of significance are put to conclude, if the differences are significant, or not.