A Toeplitz matrix is a type of matrix that looks like a checkerboard. Each row starts with the same number written multiple times. For example, if you saw a Toeplitz matrix like this:
1 1 1 1
2 2 2 2
3 3 3 3
Each row starts with the number 1, 2, or 3. So, every row looks pretty much the same. That's why it's like a checkerboard.