PCA is a technique for determining the key variables in a multidimensional data set that explain the differences in the observations (variance). Variation across multiple dimensions is difficult to interpret. PCA can be used to simplify the analysis and visualization of multidimensional data sets. In case of microarrays, it allows to summarize the ways in which gene responses vary under different conditions to expression data (where the experimental conditions are the variables, and the gene expression measurements are the observations). Examination of the components also provides insight into the underlying factors that are measured in the experiments.

For a better understanding of PCA, see this explanation

What's the role of PCA for quality control of microarray gene expression data?

PCA allows to visualize relations between variables and to assess the existence of groups of individuals and groups of variables. In that regard, it can be used to see if the sample groups separate according to prior knowledge.

What if the samples of two groups don't "separate" well?

There can be different interpretations :

• Your data is crap (worst possible outcome)
• The difference of expression caused by the difference of conditions is mild or affects only a few genes.
• Others factors, such as batch effects, impacts the expression.

Are u aware of batch effects in your data ? Have you normalized and log-transformed before performing PCA ? Do you expect the different conditions to strongly impact the transcriptome ?