The nested t test compares the means of two unmatched groups, where there is a nested factor within those treatment groups.

Are the residuals distributed according to a Gaussian distribution?

The nested t test assumes that the residuals (variation among tecnhical replicates in many cases) are sampled from a Gaussian distribution.  This assumption matters less with large samples due to the Central Limit Theorem.

The third tab of the nested t test dialog lets you plot the residuals in several ways to assess their normality.

Does the variation within each of the subcolumns have the same variance?

The nested t test assumes that the data in each subcolumn are sampled from populations with the same SD (same variance). Prism does not test this, but you can look at the data to see if this is badly violated.

Consider running the ANOVA on the logarithms of the values. In some cases this makes the variances much closer to being equal.

Is the variation among subcolumn means Gaussian?

The nested t test assumes that variation among subcolumn means is Gaussian and also that the replicates within the subcolumns are Gaussian.

Are you comparing exactly two groups?

Use the t test only to compare two groups. It is not appropriate to perform several nested t tests, comparing two treatment groups at a time.  

Do both columns contain data?

If you want to compare a single set of experimental data with a theoretical value (perhaps 100%) don't fill a column with that theoretical value and perform an unpaired t test. Instead, use a one-sample t test.

Do you really want to compare means?

The nested  t test compares the means of two groups. It is possible to have a tiny P value – clear evidence that the population means are different – even if the distributions overlap considerably. In some situations – for example, assessing the usefulness of a diagnostic test – you may be more interested in the overlap of the distributions than in differences between means.