A Burt matrix is a symmetric matrix which has one column and one row for each level (category) of each categorical variable. The entry in row i and column j is the number of observations that have the level corresponding to row i and also the level corresponding to column j. The Burt table is the result of the inner product of the indicator matrix. More specifically, if X is the indicator matrix then the corresponding Burt matrix is X'X.
Suppose there are 3 categorical variables: Gender (male, female), Hair color (blond, brown, black), and Age (under 20, from 20 to 50, over 50), arranged in the rows and columns of the Burt table in that order. Then the Burt table will have 2 + 3 + 3 = 8 rows and 8 columns. The entry in row 1 and column 1 is the number of observations that are male in both row and column, which is the number of males in the data set. The entry in row 1 and column 2 is the number of observations that are both male and female, which is 0. The entry in row 1 and column 3 is the number of observations that are both males and have blond hair, and so on.
For more information, to go Burt table.