The Kronecker product is a way to multiply two matrices together. When you multiply two matrices together, you place one above the other and then multiply each number in the top row by each number in the left column.
Then you add all of those products together, and put them in the same spot as the top row and left column. You do this for every row and column in the matrix and the result is another matrix.
The Kronecker product works a bit differently. You don't just multiply each number, but instead you multiply each row and column of the first matrix by each row and column of the second matrix. So you end up with many more numbers in the new matrix.
For example, if you have a 2x2 matrix and a 3x3 matrix, when you do the Kronecker product you will end up with a 6x6 matrix with every combination of the rows and columns from the two matrices.