The beta error is the probability of failing to reject the null hypothesis when it is actually false. In other words, it is the probability of failing to detect a true difference between the groups being compared. A low beta error means that the test has a high power to detect a true difference, while a high beta error means that the test has low power to detect a true difference.
It is generally desirable to minimize the beta error in statistical hypothesis testing, as failing to reject the null hypothesis when it is actually false can lead to incorrect conclusions about the data.