To analyze the given data and determine which judgment is incorrect, we proceed step by step as follows:

1. Calculate the Mean:
$$Mean = \frac{10 + 8 + 6 + 9 + 8 + 7 + 8}{7} = \frac{56}{7} = 8$$
Therefore, judgment C, stating that the mean is $8$, is correct.

2. Determine the Median:
First, arrange the data in ascending order: $6, 7, 8, 8, 8, 9, 10$.
The median is the middle number, which is $8$.
Therefore, judgment B, stating that the median is $8$, is correct.

3. Identify the Mode:
The number $8$ appears $3$ times, which is more frequent than any other number in the set.
Therefore, judgment A, stating that the mode is $8$, is correct.

4. Calculate the Variance:
The variance formula for this sample is:
$$S^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2$$
Substituting the mean $\bar{x} = 8$ and the given values, we get:
$$S^2 = \frac{1}{7}[(10-8)^2 + (8-8)^2 + (6-8)^2 + (9-8)^2 + (8-8)^2 + (7-8)^2 + (8-8)^2]$$
Simplifying the above expression:
$$S^2 = \frac{1}{7}[4 + 0 + 4 + 1 + 0 + 1 + 0] = \frac{10}{7} = 1.42857...$$
This shows that the variance is not $8$, but approximately $1.43$.

Therefore, the judgment that is incorrect is option D, which states that the variance is $8$. Hence, the answer is $\boxed{D}$.