The Chi-Square Test, tests whether two variables in a table are significantly different, or in other words, if there are any difference between the observed frequencies (our frequencies) and the expected frequencies (the frequencies in an hypothesis of independence).
Based on the significance level expected from the Test (default value 95%) a lower p-value indicate a stronger evidence of a statistical difference between observed and expected frequencies.
For example in a table like the one in the below picture, the p-value=0.001 indicate there's a strong evidence that the distribution of the variable 'Favorite alphabet letter' is independent from 'Gender'.