A two way table, also known as a contingency table, is a structured representation of the frequency distribution of two categorical variables. It displays cell counts, which indicate the number of observations in each category combination. Marginals, the sums of each row and column, provide the overall frequencies of each variable. Using a two way table, conditional probabilities and measures of association can be calculated to assess the relationship between the variables. The Chi-square test allows for hypothesis testing to determine if there is a significant association between them.