Suppose you have n row and k columns with one parity bit for each row and one for each column.

An single error will be caught by both the row and column parity bits.

Suppose you have a double error in one row. The row parity bit would not recover the error in that row, however, both column parity bits would detect the error.

Now, suppose you have an error chaped like a corner:

E E

E -

This would be detected, but only one error, however, the entire block would be declared an error.

Suppose your error looks like:

EEE -

This is detected in both directions.

So, all three forms of error, single, double, and triple would be detected!